1. p. 270 #47-49

2. 5.4 Inverses, Contrapositives, and Indirect Reasoning

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

4. 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

5. Statement: lines m and n are not perpendicular.
Negation: lines m and n are perpendicular.

6. Do #3-8 on the worksheet

7. 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

8. 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.

9. Do 9 and 10 on worksheet

10. Equivalent Statements have the same truth value
Equivalent Statements have the same truth value. It is important to note that a conditional and its contrapositive are equivalent statements.

11. 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.

12. 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

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

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

15. Lets do 11-16 on the worksheet.

16. Identifying contradictions. Look at number 2 on worksheet

17. 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

18. Lets try 17 together.

19. Homework: p.267#1-19 all