# 5.4 Inverses, Contrapositives, and Indirect Reasoning

p. 270 #47-49 5.4 Inverses, Contrapositives, and Indirect Reasoning

Learning Target I can write the negation of a statement I can write the inverse and contrapositive of a conditional statement

The negation of a statement has the opposite truth value. Ex: Knoxville is the capital of Tennessee. F

Knoxville is not the capital of Tennessee. T Statement: lines m and n are not perpendicular.

Negation: lines m and n are perpendicular. Do #3-8 on the worksheet

Inverse: takes a conditional statement and negates both the hypothesis and conclusion. EX: If a figure is a square, then it is a rectangle.

Inverse: If a figure is not a square, then it is not a rectangle Contrapositive: takes the converse(switches hypothesis and

conclusion) of the conditional and negates both parts. EX: If a figure is a square, then it is a rectangle. Contrapositive: If a figure is not a

rectangle, then it is not a square. Do 9 and 10 on worksheet Equivalent Statements have the

same truth value. It is important to note that a conditional and its contrapositive are equivalent statements.

Indirect Reasoning: All possibilities are considered and then all but one are proved false. The remaining possibility is true. Indirect Proof: a proof involving

indirect reasoning. The first step of writing an indirect proof is to assume the opposite of what you want to prove.

EX: the shoes cost no more than \$20 The first step would be : Assume the shoes cost more than \$20 An integer n is divisible by 5

First step in an indirect proof would be: Assume the integer n is not divisible by 5

A triangle cannot contain two right angles. First step in an indirect proof: Assume a triangle contains two right angles.

Lets do 11-16 on the worksheet. Identifying contradictions. Look at number 2 on worksheet

Step 2 of an indirect proof is to show that your assumption from step 1 leads to a contradiction. Step 3 is to conclude that the assumption

must be false and therefore what you are trying to prove must be true Lets try 17 together.

Homework: p.267#1-19 all

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