Malaysia Form 4 Mathematics Chapter 4.3 and 4.4 (Mathematical Reasoning)

7/30/2019 Malaysia Form 4 Mathematics Chapter 4.3 and 4.4 (Mathematical Reasoning)

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Name: Date:

Independent Practice

1. Change the truth of the following statements by using no and not.

2. Identify two statements from a compound statement with and/ or.

3. Construct compound statements using and/or.a) 16 2 = 8.

16 = 4_______________________

b) 2 is a factor of 12.2 is a factor of 4.

____________________

c) 3 is a prime number.3 is an odd number.

_______________________

d) 4 x 3 = 12.6 x 2 = 12.

____________________

e) 2 is a prime number.2 is an even number.

_______________________

f) -2 =

83

-2 = -4 + 2

____________________

0. Underline the truth value of each statement and then determine the truthvalue of the following and statements:

a. 15 is an odd number and 16 isan even number.

i. ____________________________

ii. ____________________________

b. All squares have 4 sides andall triangles have 3 sides.

i. ____________________________

ii. ____________________________

c. 3 x 2 = 6 and 1 + 2 = 3. i. ____________________________ii. ____________________________

d. 32 equals 9 or 3 x 3 equals 9. i. ____________________________ii. ____________________________

e. 6 is a multiple of 2 or 3. i. ____________________________ii. ____________________________

a) 13 is a prime number.___________________________

b) 2 is an even number._________________________

c) 7 is an even number.___________________________

d) Octagons have 8 sides.___________________________

e) 8 + 9 = 1___________________________

f) 10 + 2 = 4___________________________

g) All tables are square.

___________________________

h) All girls like to go shopping.

___________________________

Statement 1 Statement 2 Compound statement

a) 3 x (-2) = (-6)

-> True / False

5 + 2 = 7

-> True / False

3 x (-2) = (-6) and 5 + 2 =

7

-> True / False

b) 72 = 5

-> True / False

62 = 18

-> True / False

72 = 5 and 62 = 18

-> True / False

c) p xp =p

-> True / Falsea x a x a =

a

1

3

-> True / False

p xp =p anda x a x a =

a

1

3 .

-> True / False

d) 5 is a factor of

20.

-> True / False

5 is a factor of 15.

-> True / False

5 is a factor of 20 and 15.

-> True / False

e) 18 is a multiple

of 3.-> True / False

18 is a multiple of

5.-> True / False

18 is a multiple of 3 and 5.

-> True / False


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Name: Date:

Independent Practice

1. Underline the truth value of each statement and then determine the truthvalue of the following or statements:

2. Identify the antecedent and consequent of an implication if....then.3. Write 2 implications from a compound statement,p if and only if q.

5. Construct statements in the form ofp if and only if q.

6. Find the converse of the following implications.

Statement 1 Statement 2 Compound statement

a) 3 x (-2) = (-6)

-> True / False

5 + 2 = 7

-> True / False

3 x (-2) = (-6) or 5 + 2 = 7

-> True / False

b) 72 = 5

-> True / False

62 = 18

-> True / False

72 = 5 or 62 = 18

-> True / False

c) p xp =p

-> True / Falsea x a x a =

a

1

3

-> True / False

p xp =p3 or a x a x a =

a

1

3 .

-> True / False

d) 5 is a factor of

20.

-> True / False

5 is a factor of 15.

-> True / False

5 is a factor of 20 or 15.

-> True / False

e) 18 is a multiple

of 3.

-> True / False

18 is a multiple of

5.

-> True / False

18 is a multiple of 3 or 5.

-> True / False

a) Ifx < 0, thenx is a negativenumber.

Antecedent:_______________

Consequent:______________

b) Ifx = 4, thenx + 3 = 7.

Antecedent:_______________Consequent:______________

c) Ifn + 2 = 5, then 5n = 2.


d) Ifx > 3, thenx > 5.


e) IfA B, then A B = B.


f) If Ali woke up at 7.30am, then hewould be late to school.Antecedent:_______________Consequent:______________

a. y =x + 1 if and only ifx =y1. i. ____________________________ii. ____________________________

b. a = b if and only ifa = -b. i. ____________________________ii. ____________________________

c. x > 0 if and only ifx is positive. i. ____________________________ii. ____________________________

d. Set A = Set B if and only if A B and B A.

i. ____________________________

ii. ____________________________

e. You can eat if and only if youcan finish your homework.

i. ____________________________

ii. ____________________________

a) i) If a polygon has 5 sides, then it isa pentagon.

ii) If a polygon is a pentagon, thenit has 5 sides.

_________________________

_________________________

b) i) If I take Panadol, then I amsick.ii) If I am sick, then I takePanadol.

_________________________

_________________________

c) i) Ifx + 3 = 5, thenx = 2.ii) Ifx = 2, thenx + 3 = 5.

_________________________

_________________________

d) i) Ifa = b, then b = a.ii) Ifb = a, then a = b.

_________________________

_________________________


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6. Identify the premise and conclusion of the argument.

8. Make a conclusion based on argument I, II or III.

Implications T/F Implications T/F

Ifx = 2, then -2 (x) = -4. If -2 (x) = -4, thenx = 2.

Ifx < 3, thenx < 0.

Ifx = -3, thenx4 = -7.

Ifx >y, thenyx < 0.

Ifx > 9, thenx > 11.

a A pentagon has 5 sides.ABCDE is a pentagon.Therfore, ABCDE has 5 sides.

Premise 1:................................................................................

Premise 2:................................................................................

Conclusion:..............................................................................

c. A teachers job is to teach.Miss Ho is a teacher.Therefore, her job is to teach.

Premise 1:....................................................................................................

Premise 2:....................................................................................................

Conclusion:..................................................................................................

b. Nizham likes to drive fast cars.Nizham drives a Volvo Sport.

Therefore, Volvo Sport is a

fast car.

Premise 1:................................................................................

Premise 2:................................................................................

Conclusion:..............................................................................

d. All multiples of 2 are even numbers.1 000 004 is a multiple of 2.

Then 1 000 004 is an even number.

Premise 1:.........................................

...........................................................

Premise 2:....................................................................................................

Conclusion:..................................................................................................

a Premise 1: All 4 Quantumstudents are very hardworking.

Premise 2: Burkhan is studentfrom 4 Quantum.

Conclusion:.............................

.................................................

d. Premise 1: If a boy is 15 years old,then he is a teenager.

Premise 2: Alexander is 15 yearsold.

Conclusion:.......................................

...........................................................

b. Premise 1: All multiples of 15are multiples of 30.

Premise 2: 30 is a multiple of15.

Conclusion:..............................................................................

e. Premise 1: Ifa and b are evennumbers, a and b are divisible by 2.

Premise 2: 12 and 52 are evennumbers.

Conclusion:..................................................................................................

c. Premise 1: Ifa and b are evennumbers, a and b are divisible

by 2.

Premise 2: 17 and 3 are noteven numbers.

Conclusion:.............................

.................................................

f. Premise 1: If you study at SMK (P)Methodist, then you are a girl.

Premise 2: You do NOT sutdy at

SMK (P) Methodist.

Conclusion:..................................................................................................


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Malaysia Form 4 Mathematics Chapter 4.3 and 4.4 (Mathematical Reasoning)

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