Lesson 2.4Logical Sequencing & Conditional

Statements

Objective:

Using logical sequencing and conditional statements, converse, inverse, and contrapositive.

Logical sequencing is useful to know because it helps us to think logically through a problem, and put

a solution in a form that everyone can understand and follow. (Think about your teacher explaining how to do a math problem to you…out loud…in words!)

In order to do this we use logical sequences, and we must begin with conditional statements!!!

Why are we doing this?

Conditional Statements

A conditional statement is written in the form if p, then q.

If a given condition is met (if p), then another condition is true or an event will happen (then q).

The if-clause is the hypothesis; the then-clause is the conclusion.

Conditional Statements

Ex 1.) If you don’t do your homework, then

you will get a zero.

Ex 2) Rewrite the statement in if-then form:

2.) Every multiple of 4 is also a multiple of 2.

If a number is a multiple of 4, then it is a multiple of 2.

True or False?

True

p - Hypothesis

q - Conclusion

Logical Order

When given several related conditional statements, you must put them in logical order. The conclusion of one statement will flow into the hypothesis of the next. This is what we do in a paragraph proof!!!

Logical Order – Put the following if-then statements in order

A. If Cameron graduates with a degree, then he will make a lot of money. B. If Cameron studies hard, then his grades will be good. C. If Cameron makes a lot of money, then he will be able to buy a new car. D. If Cameron attends college, then he will graduate with a degree. E. If Cameron has good grades, then he will be able to attend college.

Logical Order: B. If Cameron studies hard, then his grades will be good. E. If Cameron has good grades, then he will be able to attend college. D. If Cameron attends college, then he will graduate with a degree. A. If Cameron graduates with a degree, then he will make a lot of money. C. If Cameron makes a lot of money, then he will be able to buy a new car.

Conclusion: If Cameron studies hard, then he will be able to buy a new car.

This is an example of a SYLLOGISM – it is just a logical progression, you will do one on your homework

Logical Order Ex. 2 – Put the statements in logical order. A. If a shape is a square, then it is a rhombus. B. If a shape is a parallelogram , then it is a quadrilateral. C. If a shape is a quadrilateral, then it is a polygon. D. If a shape is a rhombus, then it is a parallelogram.

A. If a shape is a square, then it is a rhombus. D. If a shape is a rhombus, then it is a parallelogram. B. If a shape is a parallelogram , then it is a quadrilateral. C. If a shape is a quadrilateral, then it is a polygon.

Conclusion: If a shape is a square, then it is a polygon.

Converse

The converse of a conditional statement is formed by switching the places of the hypothesis and conclusion.

The sentence if p, then q

becomes if q, then p.

What is the converse?

Is the given statement true or false? Write the converse statement for each conditional statement. Is the converse true or false? If the converse is false, come up with a counter example.

Examples:

1. If a quadrilateral is a rectangle, then it is a parallelogram. TRUE

If a quadrilateral is a parallelogram, then it is a rectangle. FalseIt could be a rhombus

Inverse

The inverse of a conditional statement is formed by negating the hypothesis and the conclusion.

The sentence if p, then q becomes if not p, then not q.

What is the Inverse?

Ex: If it is sunny outside, then I will go running.

Becomes… If it is not sunny outside, then I will not go running.

Is the given statement true or false? Write the inverse statement for each conditional statement.

Is the inverse true or false? If the inverse is false, come up with a counter example.

4. Example: If two lines are perpendicular, then they intersect. TRUE

False

If two lines are not perpendicular, then they don’t intersect.

Contrapositive

The contrapositive of a conditional statement is formed in two steps.

1. Form the converse of the statement 2. Form the inverse of the converse.

In other words, the sentence if p, then q becomes if not q, then not p.

What is a contrapositive Statement

Is the given statement true or false? Write the contrapositive statement for each conditional statement. Is the contrapositive true or false? If the contrapositive is false, come up with a counter example.

Examples

7. If a polygon has just four sides, then it is a quadrilateral.

If it is not a quadrilateral, then it is not a polygon with four sides.

TRUE

TRUE

8. If 2 angles form a straight line, then their sum is .180

TRUE

If the sum is not , then the 2 angles don’t form a straight line.

180

TRUE

When will they be true:

If your original is true then your _____________is usually true

and usually your ____________and ___________ will be __________

contrapositive

FALSE

inverseconverse

When will they be true:

If your original is false then your _____________is false

and usually your ____________and ___________ will be __________

contrapositive

TRUE

inverseconverse

Homework

Worksheet 2.4 and Syllogism Poster

Your syllogism poster is easier than you think!!....