Use set notation to list all of the elements of this set: {y : y is an even natural number less than...

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Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice Exercises

Transcript of Use set notation to list all of the elements of this set: {y : y is an even natural number less than...

Page 1: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set notation to list all of the elements of this set:{y : y is an even natural number less than 6}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Page 2: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Use set notation to list all of the elements of this set:{y : y is an even natural number less than 6}

‘Natural number’ is another name the for ‘counting number’ { 1, 2, 3, … }

Page 3: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Use set notation to list all of the elements of this set:{y : y is an even natural number less than 6}

‘Natural number’ is another name the for ‘counting number’ { 1, 2, 3, … }

Page 4: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Use set notation to list all of the elements of this set:{y : y is an even natural number less than 6}

‘Natural number’ is another name the for ‘counting number’ { 1, 2, 3, … }

{ 1 , 2 , 3, 4 , 5 }

Page 5: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Use set notation to list all of the elements of this set:{y : y is an even natural number less than 6}

‘Natural number’ is another name the for ‘counting number’ { 1, 2, 3, … }

{ 1 , 2 , 3, 4 , 5 } X X X

Page 6: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Use set notation to list all of the elements of this set:{y : y is an even natural number less than 6}

‘Natural number’ is another name the for ‘counting number’ { 1, 2, 3, … }

{ 1 , 2 , 3, 4 , 5 }

Page 7: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set notation to list all of the elements of this set:{y : y is an even natural number less than 6}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

‘Natural number’ is another name the for ‘counting number’ { 1, 2, 3, … }

{ 2 , 4 }

Page 8: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set notation to list all of the elements of this set:

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{-21, -17, -13, … , 7}

Page 9: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set notation to list all of the elements of this set:

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

First notice that these numbers are 4 units apart.

4 4

{-21, -17, -13, … , 7}

{-21, -17, -13, … , 7}

Page 10: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set notation to list all of the elements of this set:

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

So the next number is -9.

44 4

{-21, -17, -13, -9, … , 7}

{-21, -17, -13, … , 7}

Page 11: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set notation to list all of the elements of this set:

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

And the next number is -5.

44 4

{-21, -17, -13, -9, -5, … , 7}

4

{-21, -17, -13, … , 7}

Page 12: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set notation to list all of the elements of this set:

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

And the next number is -1.

44 4

{-21, -17, -13, -9, -5, -1, … , 7}

4 4

{-21, -17, -13, … , 7}

Page 13: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set notation to list all of the elements of this set:

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

And the next number is 3.

44 4

{-21, -17, -13, -9, -5, -1, 3, 7}

4 4 4

{-21, -17, -13, … , 7}

Page 14: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set notation to list all of the elements of this set:

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

And 3+4=7 so we’re done.

44 4

{-21, -17, -13, -9, -5, -1, 3, 7}

4 4 4 4

{-21, -17, -13, … , 7}

Page 15: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set notation to list all of the elements of this set:

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{-21, -17, -13, -9, -5, -1, 3, 7}

{-21, -17, -13, … , 7}

Page 16: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set-builder notation to express this set:{6, 12, 18, 24, …}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Page 17: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set-builder notation to express this set:{6, 12, 18, 24, …}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{x : x is a natural number and a multiple of 6 }

Page 18: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Use set-builder notation to express this set:{6, 12, 18, 24, …}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{x : x is a natural number and a multiple of 6 }

Page 19: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Is this set well defined?{t : t has a nice house}

Page 20: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

DO NOT OVERTHINK THESE TYPE OF QUESTIONS!!

Is this set well defined?{t : t has a nice house}

Page 21: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

DO NOT OVERTHINK THESE TYPE OF QUESTIONS!!No one is trying to trick you here.

Is this set well defined?{t : t has a nice house}

Page 22: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

DO NOT OVERTHINK THESE TYPE OF QUESTIONS!!No one is trying to trick you here.

A set is well defined if it is possible to determine if a given object is included in the set.

Is this set well defined?{t : t has a nice house}

Page 23: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

DO NOT OVERTHINK THESE TYPE OF QUESTIONS!!No one is trying to trick you here.

A set is well defined if it is possible to determine if a given object is included in the set.

Without overthinking this,

Is this set well defined?{t : t has a nice house}

Page 24: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

DO NOT OVERTHINK THESE TYPE OF QUESTIONS!!No one is trying to trick you here.

A set is well defined if it is possible to determine if a given object is included in the set.

Without overthinking this,

Is this set well defined?{t : t has a nice house}

Most would probably agree that the meaning of

‘nice’ varies a lot from person to person so it

would be hard to think of the set being well defined.

Page 25: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Is this set well defined?{t : t has a nice house}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

DO NOT OVERTHINK THESE TYPE OF QUESTIONS!!No one is trying to trick you here.

A set is well defined if it is possible to determine if a given object is included in the set.

Without overthinking this,NO, this set is not well defined.

Most would probably agree that the meaning of

‘nice’ varies a lot from person to person so it

would be hard to think of the set being well defined.

Page 26: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Is this set well defined?{x : x lives in Texas}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Page 27: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Is this set well defined?{x : x lives in Texas}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

DO NOT OVERTHINK THESE TYPE OF QUESTIONS!!No one is trying to trick you here.

Page 28: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Is this set well defined?{x : x lives in Texas}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

DO NOT OVERTHINK THESE TYPE OF QUESTIONS!!No one is trying to trick you here.

A set is well defined if it is possible to determine if a given object is included in the set.

Page 29: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Is this set well defined?{x : x lives in Texas}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

DO NOT OVERTHINK THESE TYPE OF QUESTIONS!!No one is trying to trick you here.

A set is well defined if it is possible to determine if a given object is included in the set.

Without overthinking this,

The Texas border is fixed, and although, if you think

hard enough, you might be able to imagine a situation where it wouldn’t be clear

that a person did or did not live in Texas, we aren’t

supposed to have to do that.

Page 30: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Is this set well defined?{x : x lives in Texas}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

DO NOT OVERTHINK THESE TYPE OF QUESTIONS!!No one is trying to trick you here.

A set is well defined if it is possible to determine if a given object is included in the set.

Without overthinking this,

The Texas border is fixed, and although, if you think

hard enough, you might be able to imagine a situation where it wouldn’t be clear

that a person did or did not live in Texas, we aren’t

supposed to have to do that.

Page 31: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Is this set well defined?{x : x lives in Texas}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

DO NOT OVERTHINK THESE TYPE OF QUESTIONS!!No one is trying to trick you here.

A set is well defined if it is possible to determine if a given object is included in the set.

Without overthinking this, YES, this set is well defined.

The Texas border is fixed, and although, if you think

hard enough, you might be able to imagine a situation where it wouldn’t be clear

that a person did or did not live in Texas, we aren’t

supposed to have to do that.

Page 32: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Replace ‘#’ with ‘’ or ‘ ’ to make the statement true: 16 # {x : x is a rational number}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Page 33: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Replace ‘#’ with ‘’ or ‘ ’ to make the statement true: 16 # {x : x is a rational number}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

A ‘rational number’ is one that can be written as a RATIO of two integers.

Page 34: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Replace ‘#’ with ‘’ or ‘ ’ to make the statement true: 16 # {x : x is a rational number}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

And remember, the set of integers is the set of counting numbers (the positive integers) plus the set of negative integers plus zero.

{ … ,-3 , -2 , -1 , 0 , 1 , 2 , 3 , … }

A ‘rational number’ is one that can be written as a RATIO of two integers.

Page 35: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Replace ‘#’ with ‘’ or ‘ ’ to make the statement true: 16 # {x : x is a rational number}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

And remember, the set of integers is the set of counting numbers (the positive integers) plus the set of negative integers plus zero.

{ … ,-3 , -2 , -1 , 0 , 1 , 2 , 3 , … }

A ‘rational number’ is one that can be written as a RATIO of two integers.

16 can be written as the ratio of two integers in many ways:

Page 36: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Replace ‘#’ with ‘’ or ‘ ’ to make the statement true: 16 # {x : x is a rational number}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

And remember, the set of integers is the set of counting numbers (the positive integers) plus the set of negative integers plus zero.

{ … ,-3 , -2 , -1 , 0 , 1 , 2 , 3 , … }16 can be written as the ratio of two integers in many ways:

For example, as or

A ‘rational number’ is one that can be written as a RATIO of two integers.

Page 37: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Replace ‘#’ with ‘’ or ‘ ’ to make the statement true: 16 # {x : x is a rational number}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

And remember, the set of integers is the set of counting numbers (the positive integers) plus the set of negative integers plus zero.

{ … ,-3 , -2 , -1 , 0 , 1 , 2 , 3 , … }16 can be written as the ratio of two integers in many ways:

For example, as or … so, 16 is a rational number.

A ‘rational number’ is one that can be written as a RATIO of two integers.

Page 38: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Replace ‘#’ with ‘’ or ‘ ’ to make the statement true: 16 {x : x is a rational number}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

And remember, the set of integers is the set of counting numbers (the positive integers) plus the set of negative integers plus zero.

{ … ,-3 , -2 , -1 , 0 , 1 , 2 , 3 , … }16 can be written as the ratio of two integers in many ways:

For example, as or … so, 16 is a rational number.

A ‘rational number’ is one that can be written as a RATIO of two integers.

Page 39: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Replace ‘#’ with ‘’ or ‘ ’ to make the statement true: 16 {x : x is a rational number}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

And remember, the set of integers is the set of counting numbers (the positive integers) plus the set of negative integers plus zero.

{ … ,-3 , -2 , -1 , 0 , 1 , 2 , 3 , … }16 can be written as the ratio of two integers in many ways:

For example, as or … so, 16 is a rational number.

A ‘rational number’ is one that can be written as a RATIO of two integers.

Page 40: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {103, 104, 105, 106, … , 123}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Page 41: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {103, 104, 105, 106, … , 123}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

Page 42: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {103, 104, 105, 106, … , 123}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

So, we just need to count the elements in A.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

Page 43: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {103, 104, 105, 106, … , 123}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

So, we just need to count the elements in A.Shortcut for counting CONSECUTIVE integers:

LARGEST – SMALLEST + 1

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

Page 44: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {103, 104, 105, 106, … , 123}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

So, we just need to count the elements in A.

For example, if U = { 4 , 5, 6 }, then n(U) = 6 – 4 + 1 = 3.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

Shortcut for counting CONSECUTIVE integers:LARGEST – SMALLEST + 1

Page 45: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {103, 104, 105, 106, … , 123}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

So, we just need to count the elements in A.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

LargestSmallest

Shortcut for counting CONSECUTIVE integers:LARGEST – SMALLEST + 1

Page 46: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {103, 104, 105, 106, … , 123}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

So, we just need to count the elements in A.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

LargestSmallest

Shortcut for counting CONSECUTIVE integers:LARGEST – SMALLEST + 1

So, n(A) = 123 – 103 + 1

Page 47: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {103, 104, 105, 106, … , 123}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

So, we just need to count the elements in A.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

So, n(A) = 123 – 103 + 1n(A) = 21

Shortcut for counting CONSECUTIVE integers:LARGEST – SMALLEST + 1

Page 48: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {x : x is a woman who served as U.S. Vice President before 1900}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Page 49: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {x : x is a woman who served as U.S. Vice President before 1900}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

I hope that you know without having to ask YAHOO! answers like this person did:

Page 50: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {x : x is a woman who served as U.S. Vice President before 1900}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Who was the first female vice president in the USA?

I hope that you know without having to ask YAHOO! answers like this person did:

Page 51: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {x : x is a woman who served as U.S. Vice President before 1900}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Who was the first female vice president in the USA?

I hope that you know without having to ask YAHOO! answers like this person did:

Best Answer (from Matt)There has never been a female Vice President of the USA. There has, however, been a Democratic nominee, Geraldine Ferraro, whose Dukakis ticket lost the 1984 election by a wide margin to Ronald Reagan and George HW Bush.

Page 52: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {x : x is a woman who served as U.S. Vice President before 1900}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Who was the first female vice president in the USA?

I hope that you know without having to ask YAHOO! answers like this person did:

Best Answer (from Matt)There has never been a female Vice President of the USA. There has, however, been a Democratic nominee, Geraldine Ferraro, whose Dukakis ticket lost the 1984 election by a wide margin to Ronald Reagan and George HW Bush.

Page 53: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {x : x is a woman who served as U.S. Vice President before 1900}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Who was the first female vice president in the USA?

I hope that you know without having to ask YAHOO! answers like this person did:

Best Answer (from Matt)There has never been a female Vice President of the USA. There has, however, been a Democratic nominee, Geraldine Ferraro, whose Dukakis ticket lost the 1984 election by a wide margin to Ronald Reagan and George HW Bush.

Page 54: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {x : x is a woman who served as U.S. Vice President before 1900}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Who was the first female vice president in the USA?

I hope that you know without having to ask YAHOO! answers like this person did:

Best Answer (from Matt)There has never been a female Vice President of the USA. There has, however, been a Democratic nominee, Geraldine Ferraro, whose Dukakis ticket lost the 1984 election by a wide margin to Ronald Reagan and George HW Bush.

Page 55: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {x : x is a woman who served as U.S. Vice President before 1900}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Who was the first female vice president in the USA?

I hope that you know without having to ask YAHOO! answers like this person did:

Best Answer (from Matt)There has never been a female Vice President of the USA. There has, however, been a Democratic nominee, Geraldine Ferraro, whose Dukakis ticket lost the 1984 election by a wide margin to Ronald Reagan and George HW Bush.

Page 56: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Find n(A) for the following set A.A = {x : x is a woman who served as U.S. Vice President before 1900}

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

I hope that you know without having to ask YAHOO! answers like this person did:

n(A) = 0

Page 57: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}

Page 58: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

A set is finite if its cardinal number is a whole number.An infinite set is one that is not finite.

Page 59: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

A set is finite if its cardinal number is a whole number.An infinite set is one that is not finite.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}

The set of whole numbers are the

counting numbers PLUS zero.

Page 60: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

A set is finite if its cardinal number is a whole number.An infinite set is one that is not finite. The set of whole

numbers are the counting numbers

PLUS zero.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}

{ 0 , 1 , 2 , 3, 4 , … }

Page 61: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

A set is finite if its cardinal number is a whole number.An infinite set is one that is not finite. The set of whole

numbers are the counting numbers

PLUS zero.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}

{ 0 , 1 , 2 , 3, 4 , … }

{All multiples of 4 that are greater than 19} =

Page 62: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

A set is finite if its cardinal number is a whole number.An infinite set is one that is not finite. The set of whole

numbers are the counting numbers

PLUS zero.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}

{ 0 , 1 , 2 , 3, 4 , … }

{All multiples of 4 that are greater than 19} ={ 20, 24, 28, 32, 36, … }

Page 63: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

A set is finite if its cardinal number is a whole number.An infinite set is one that is not finite. The set of whole

numbers are the counting numbers

PLUS zero.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}

{ 0 , 1 , 2 , 3, 4 , … }

{All multiples of 4 that are greater than 19} ={ 20, 24, 28, 32, 36, … }

Page 64: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

A set is finite if its cardinal number is a whole number.An infinite set is one that is not finite. The set of whole

numbers are the counting numbers

PLUS zero.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}

{ 0 , 1 , 2 , 3, 4 , … }

{All multiples of 4 that are greater than 19} ={ 20, 24, 28, 32, 36, … }

Page 65: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

A set is finite if its cardinal number is a whole number.An infinite set is one that is not finite. The set of whole

numbers are the counting numbers

PLUS zero.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}

{ 0 , 1 , 2 , 3, 4 , … }

{All multiples of 4 that are greater than 19} ={ 20, 24, 28, 32, 36, … }

Page 66: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

A set is finite if its cardinal number is a whole number.An infinite set is one that is not finite. The set of whole

numbers are the counting numbers

PLUS zero.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}

{ 0 , 1 , 2 , 3, 4 , … }

{All multiples of 4 that are greater than 19} ={ 20, 24, 28, 32, 36, … }

Page 67: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

A set is finite if its cardinal number is a whole number.An infinite set is one that is not finite. The set of whole

numbers are the counting numbers

PLUS zero.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}

{ 0 , 1 , 2 , 3, 4 , … }

{All multiples of 4 that are greater than 19} ={ 20, 24, 28, 32, 36, … }

Page 68: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

The number of elements in set A is called the cardinal number of set A.The cardinal number of a set A is denoted n(A).

A set is finite if its cardinal number is a whole number.An infinite set is one that is not finite. The set of whole

numbers are the counting numbers

PLUS zero.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}

{ 0 , 1 , 2 , 3, 4 , … }

{All multiples of 4 that are greater than 19} ={ 20, 24, 28, 32, 36, … } INFINITE

Page 69: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

{y : y is a number between 7 and 14}

Page 70: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number

{y : y is a number between 7 and 14}

Page 71: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number 𝟏𝟎𝟏𝟏𝟎

{y : y is a number between 7 and 14}

Page 72: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number

10110

{y : y is a number between 7 and 14}

Page 73: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number 𝟖

10110

{y : y is a number between 7 and 14}

Page 74: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number

10110 8

{y : y is a number between 7 and 14}

Page 75: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number .1

10110 8

{y : y is a number between 7 and 14}

Page 76: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number

10110 8 .1

{y : y is a number between 7 and 14}

Page 77: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number .0001

10110 8 .1

{y : y is a number between 7 and 14}

Page 78: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number .0001

10110 8 .1

{y : y is a number between 7 and 14}

Page 79: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number .999907

10110 8 .1

.0001

{y : y is a number between 7 and 14}

Page 80: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number

.999907

10110 8 .1

.0001

{y : y is a number between 7 and 14}

Page 81: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number 3.4

10110 8 .1

.0001.999907

{y : y is a number between 7 and 14}

Page 82: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number 3.4

10110 8 .1

.0001.999907

{y : y is a number between 7 and 14}

Page 83: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number 3.4

10110 8 .1

.0001.999907

{y : y is a number between 7 and 14}

Page 84: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

Number is a very generic term so this

could be ANY number 3.4

10110 8 .1

.0001.999907

INFINITE

{y : y is a number between 7 and 14}

Page 85: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

{y : y is a number between 7 and 14}

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

INFINITE

Page 86: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

{y : y is a number between 7 and 14}

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

INFINITE{y : y is an integer between 7 and 14}

Page 87: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

{y : y is a number between 7 and 14}

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

INFINITE{y : y is an integer between 7 and 14}

= { 8 , 9 , 10 , 11 , 12 , 13 }

Page 88: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

{y : y is a number between 7 and 14}

Describe the following set as either finite or infinite.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

{All multiples of 4 that are greater than 19}INFINITE

INFINITE{y : y is an integer between 7 and 14}

= { 8 , 9 , 10 , 11 , 12 , 13 }FINITE

Page 89: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Use table info below to describe this set in an alternative way:{Class A, Class B, Class D, Class E, Class F}

Humanities Writing Culture DiversityClass A Yes Yes Yes YesClass B Yes Yes Yes YesClass C No No Yes NoClass D Yes Yes No NoClass E Yes No Yes YesClass F Yes No No NoClass G No No No Yes

Page 90: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Humanities Writing Culture DiversityClass A Yes Yes Yes YesClass B Yes Yes Yes YesClass C No No Yes NoClass D Yes Yes No NoClass E Yes No Yes YesClass F Yes No No NoClass G No No No Yes

Use table info below to describe this set in an alternative way:{Class A, Class B, Class D, Class E, Class F}

Page 91: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Humanities Writing Culture DiversityClass A Yes Yes Yes YesClass B Yes Yes Yes YesClass C No No Yes NoClass D Yes Yes No NoClass E Yes No Yes YesClass F Yes No No NoClass G No No No Yes

Use table info below to describe this set in an alternative way:{Class A, Class B, Class D, Class E, Class F}

Page 92: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Humanities Writing Culture DiversityClass A Yes Yes Yes YesClass B Yes Yes Yes YesClass C No No Yes NoClass D Yes Yes No NoClass E Yes No Yes YesClass F Yes No No NoClass G No No No Yes

Use table info below to describe this set in an alternative way:{Class A, Class B, Class D, Class E, Class F}

Page 93: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Humanities Writing Culture DiversityClass A Yes Yes Yes YesClass B Yes Yes Yes YesClass C No No Yes NoClass D Yes Yes No NoClass E Yes No Yes YesClass F Yes No No NoClass G No No No Yes

Use table info below to describe this set in an alternative way:{Class A, Class B, Class D, Class E, Class F}

Page 94: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Humanities Writing Culture DiversityClass A Yes Yes Yes YesClass B Yes Yes Yes YesClass C No No Yes NoClass D Yes Yes No NoClass E Yes No Yes YesClass F Yes No No NoClass G No No No Yes

Use table info below to describe this set in an alternative way:{Class A, Class B, Class D, Class E, Class F}

Page 95: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Humanities Writing Culture DiversityClass A Yes Yes Yes YesClass B Yes Yes Yes YesClass C No No Yes NoClass D Yes Yes No NoClass E Yes No Yes YesClass F Yes No No NoClass G No No No Yes

Use table info below to describe this set in an alternative way:{Class A, Class B, Class D, Class E, Class F}

Page 96: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Humanities Writing Culture DiversityClass A Yes Yes Yes YesClass B Yes Yes Yes YesClass C No No Yes NoClass D Yes Yes No NoClass E Yes No Yes YesClass F Yes No No NoClass G No No No Yes

Use table info below to describe this set in an alternative way:{Class A, Class B, Class D, Class E, Class F}

Page 97: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Humanities Writing Culture DiversityClass A Yes Yes Yes YesClass B Yes Yes Yes YesClass C No No Yes NoClass D Yes Yes No NoClass E Yes No Yes YesClass F Yes No No NoClass G No No No Yes

Use table info below to describe this set in an alternative way:{Class A, Class B, Class D, Class E, Class F}

Page 98: Use set notation to list all of the elements of this set: {y : y is an even natural number less than 6} MATH 110 Sec 2-1: The Language of Sets Practice.

MATH 110 Sec 2-1: The Language of SetsPractice Exercises

Humanities Writing Culture DiversityClass A Yes Yes Yes YesClass B Yes Yes Yes YesClass C No No Yes NoClass D Yes Yes No NoClass E Yes No Yes YesClass F Yes No No NoClass G No No No Yes

Use table info below to describe this set in an alternative way:{Class A, Class B, Class D, Class E, Class F}

{ x : x is a Humanities class }