1. 2-3 C ONDITIONALS

2. S TATEMENTS Conditional statement A statement that can be written in if-then form If-Then statement If p, then q “p” and “q” are statements “p” is the hypothesis “q” is the conclusion

3. E XAMPLE Identify the hypothesis and conclusion of the following statement. Answer:Hypothesis: A polygon has 6 sides. Conclusion: It is a hexagon. If a polygon has 6 sides, then it is a hexagon. hypothesis conclusion

4. E XAMPLE A.Hypothesis: You will cry. Conclusion: You are a baby. B.Hypothesis: You are a baby. Conclusion: You will cry. C.Hypothesis: Babies cry. Conclusion: You are a baby. D.none of the above Which of the choices correctly identifies the hypothesis and conclusion of the given conditional? If you are a baby, then you will cry.

5. E XAMPLE Write a Conditional in If-Then Form Write the statement in if-then form. Then identify the hypothesis and conclusion of the statement. A five-sided polygon is a pentagon. Answer:If a polygon has five sides, then it is a pentagon. Hypothesis: A polygon has five sides. Conclusion: It is a pentagon.

6. E XAMPLE A.If an angle is acute, then it measures less than 90°. B.If an angle is not obtuse, then it is acute. C.If an angle measures 45°, then it is an acute angle. D.If an angle is acute, then it measures 45°. Which of the following is the correct if-then form of the given statement? An angle that measures 45° is an acute angle.

7. E XAMPLE Truth Values of Conditionals Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample. If last month was February, then this month is March. True; March is the month that follows February.

8. E XAMPLE Determine the truth value of the conditional statement. If true, explain your reasoning. If false, give a counterexample. The product of whole numbers is greater than or equal to 0. A.True; 3 ● 5 = 15, 8 ● 2 = 16 B.False; –3 ● 4 = –12

9. C ONVERSE Switch the “if” and “then” Think opposite, or CON-artist 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

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

11. P: HYPOTHESIS Q: CONCLUSION Recall: StatementIf p, then q Recall: ConverseIf q, then p (con-artist—does a switch) InverseIf not p, then not q Add a word In---not ContrapositiveIf not q, then not p Weirdest word—so do both, add NOT and Switch

12. EXAMPLES: Give the Converse, Inverse and Contrapos. State Tor F If a parallelogram is a square, then it is a rectangle. (T) C: If a parallelogram is a rectangle, then it is a square. (F) I: If a parallelogram is not a square, then it is not a rectangle (F) C+: If a parallelogram is not a rectangle, then it is not a square (T)

13. RULE!!!!!!!!!!!!!! Related conditionals A conditional statement and its contrapositive are logically equivalent. Either both are true or both are false. - The converse and the inverse are logically equivalent. Either both are true or both are false.

14. H OMEWORK ! ( WRITE IT DOWN !!!!!!!!) Pg.111 #19-51 odd(skip #41) 53-56, 58-61, 68 ALL ON a Separate paper!!!!!!!!!!!