2-3 C ONDITIONALS. 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.

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2-3 C ONDITIONALS

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

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

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.

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.

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.

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.

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

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

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

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

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)

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.

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