Use a proof by contrapositive to show that for all integers a ∈ Z, if a3 is even, then a − 1 is odd. Justify all of yoursteps.

Question

Use a proof by contrapositive to show that for all integers a ∈ Z, if a3 is even, then a − 1 is odd. Justify all of yoursteps.
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Solution 1

Proof by contrapositive involves proving that if the conclusion is false, then the premise must also be false.

The contrapositive of the statement "if a^3 is even, then a - 1 is odd" is "if a - 1 is not odd (i.e., even), then a^3 is not even (i.e., odd)".

Here's the proof:

  1. Assume that a - 1 i Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
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