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Get Full Access to Discrete Mathematics With Applications - 4 Edition - Chapter 4.6 - Problem 28e
Get Full Access to Discrete Mathematics With Applications - 4 Edition - Chapter 4.6 - Problem 28e

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# Prove each of the statement in two ways: (a) | Ch 4.6 - 28E

ISBN: 9780495391326 48

## Solution for problem 28E Chapter 4.6

Discrete Mathematics with Applications | 4th Edition

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Problem 28E

Prove each of the statement in two ways: (a) by contraposition and (b) by contradiction.ExerciseFor all integers m and n, if mn is even then m is even or n is even.

Step-by-Step Solution:

Solution:Step 1:In this question it is required to prove that for all integers m and n, if mn is even then m is even or n is even by contraposition and contradiction.(a)Step 2:The given statement is “For all integers m and n, if mn is even then m is even or n is even.”. The contrapositive of the above statement is “For all integers m and n, if is odd, then both of and are odd”.Now we can prove the contrapositive of the given statement using direct method of proof.Since is odd, it requires that both and are odd as Therefore, the given statement is true since its contrapositive is true.(b)

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