Chapter 2 Geometric Reasoning

1. Chapter 2 Geometric Reasoning 2.2 Conditional Statements

2. Objectives I can identify, write, and analyze the truth value of a conditional statement. I can write the inverse, converse, and contrapositive of a conditional statement.

3. Introduction In chapter 2, we will discuss how we use logic to develop mathematical proofs. When writing proofs, it is important to use exact and correct mathematical language. We must say what we mean!

4. Introduction Do you recognize the following conversation?

7. Charles Dodgson Charles Dodgson lived from 1832 to 1898 Dodgson was a mathematics lecturer and author of mathematics books who is better known by the pseudonym Lewis Carroll. He is known especially for Alice's Adventures in Wonderland.

8. 2.2 Conditional Statements In order to analyze statements, we will translate them into a logic statement called a conditional statement. (You will be taking notes now)

9. Essential Question: How do I recognize and analyze a conditional statement?

10. 2.2 Conditional Statements A _________________ is a statement that can be expressed in ________form.

11. 2.2 Conditional Statements Example:

12. 2.2 Conditional Statements To fully analyze this conditional statement, we need to find three new conditionals: Converse Inverse Contrapositive

13. 2.2 Conditional Statements The ________ of a conditional statement is formed by switching the hypothesis and the conclusion. Example:

14. 2.2 Conditional Statements The ________ of a conditional statement is formed by negating (inserting �not�) the hypothesis and the conclusion. Example:

15. 2.2 Conditional Statements The ______________ of a conditional statement is formed by negating the hypothesis and the conclusion of the converse. Example: (Converse) If I am breathing, then I am sleeping. (Contrapositive) If I am not breathing, then I am not sleeping.

16. 2.2 Conditional Statements

17. 2.2 Conditional Statements The conditional statement, inverse, converse and contrapositive all have a truth value. That is, we can determine if they are true or false. When two statements are both true or both false, we say that they are logically equivalent.

18. 2.2 Conditional Statements

19. 2.2 Conditional Statements The conditional statement and its contrapositive have the same truth value. They are both true. They are logically equivalent.

20. 2.2 Conditional Statements The inverse and the converse have the same truth value. They are both false. They are logically equivalent.

21. Practice Translate the following statement into a conditional statement. Then find the converse, inverse and contrapositive. �A cloud of steam can be seen when the space shuttle is launched�

22. �A cloud of steam can be seen when the space shuttle is launched�

23. 1. Identify the underlined portion of the conditional statement. hypothesis Conclusion neither

24. 2. Identify the underlined portion of the conditional statement. hypothesis Conclusion neither

25. 3. Identify the underlined portion of the conditional statement. hypothesis Conclusion neither

26. 4. Identify the converse for the given conditional. If you do not like tennis, then you do not play on the tennis team. If you play on the tennis team, then you like tennis. If you do not play on the tennis team, then you do not like tennis. You play tennis only if you like tennis.

27. 5. Identify the inverse for the given conditional. If 2x is not even, then x is not odd. If 2x is even, then x is odd. If x is even, then 2x is odd. If x is not odd, then 2x is not even.

28. 2.2 Conditional Statements Exit assignment: Write this statement as a conditional statement. Identify the hypothesis and conclusion by underlining the hypothesis with one line and the conclusion with two lines. HW: 13-23 on p. 85.