2-1 I F -T HEN S TATEMENTS AND C ONVERSES  Chapter 2 Test: Monday Oct. 1 st  Quiz: Wed. Sept. 26  Start today’s notes in current notes section.

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2-1 I F -T HEN S TATEMENTS AND C ONVERSES  Chapter 2 Test: Monday Oct. 1 st  Quiz: Wed. Sept. 26  Start today’s notes in current notes section

S TATEMENTS Conditional statement The conclusion depends on what the hypothesis is If-Then statement If p, then q “p” and “q” are statements “p” is the hypothesis “q” is the conclusion Other ways to write an if-then statement p implies q q if p (special case: “if” is in the middle. Be careful!)

C ONVERSE Switch the “if” and “then” Think opposite If q, then p. Example: If today is Friday, then tomorrow is Saturday True Converse If tomorrow is Saturday, then today is Friday True Underline hypothesis once Underline conclusion twice

E XAMPLE 2 If I live in Anaheim, then I live in California True Converse If I live in California, then I live in Anaheim False When you are trying to figure out if it is true or false, assume that the hypothesis is true and try to make the conclusion false This is called a counterexample Counterexample: I live in Los Alamitos

TOO Think of your own “if-then” statement where the original statement is true, but the converse is false Anyone want to share???

E XAMPLE : WRITING A DEFINITION, if B is the midpoint of AC Re-write in “if-then” form: If B is the midpoint of AC, then Converse: If, then B is the midpoint of AC. Is the converse true? Can you think of a counterexample? A B C

B I C ONDITIONAL “Bi” means 2 – two “if-then” statements that are converses of each other. If both the statements are true, then you can rewrite it as one statement Use the phrase “if and only if” (abbrv: “iff”) Too: Re-write the first example as a biconditional Today is Friday if and only if tomorrow is Saturday.

H OMEWORK Page 35 #1-29 odd Be sure to read the directions! Flashcards! If-Then statement Hypothesis Conclusion Converse Biconditional Counterexample