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Question: exercise 24 i think that i have the answer i...

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that a2 is both an even number and not an even number. This is a contradiction. Hence we ust rejeet our assumption that a is not an even number, so we conclude that indeed a is an even number. We have proved this under the assumption that a2 is an even number. Discharging this assumption, we conclude that the conditional sentence (7) is true The Contrapositive of a Conditional Sentence Given a conditional sentence P Q, the related conditional sentence . Q P is called the contro positive o P . A conditional sentence and its contrapositive are logically equivalent, as the ollowing truth table shows: TİT TİF FİT TİF It is important not to confuse the contrapositive of P Q with the converse of P Q. The contrapositive of P Q is-Q 극-P. The converse of F-Q is Q P. The contrapositive, ﹁o-,-P, is logically equivalent to P Q, but the converse, Q P, is not. Exercise 24. Let A be the conditional sentence If x 2 and y 3, then ry 6. Write out the contrapositive of A in words. Is the contrapositive of A true? Write out the converse of A in words. Is the converse of A true, or is it impossible to say without further information about the specific values of z and y? (Hint: Can you find specific values for a and y for which the converse of A is true? If so, give an example of such values. Can you find other specific values for z and y for which the converse of A is false? If so, give an example of such values.) (a) (b) Copyright Neil Falkner 2018

Exercise 24. I think that I have the answer I just want to make sure.

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