Let 𝑛 be an integer. Prove that if 3𝑛 + 2 is even, then 𝑛 is even usinga) a proof by contraposition.b) a proof by contradictio

Question

Let 𝑛 be an integer. Prove that if 3𝑛 + 2 is even, then 𝑛 is even usinga) a proof by contraposition.b) a proof by contradictio
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Solution 1

a) Proof by contraposition:

The contrapositive of the statement "if 3n + 2 is even, then n is even" is "if n is not even (i.e., n is odd), then 3n + 2 is not even (i.e., 3n + 2 is odd)".

Let's assume n is odd. Then, n can be written as 2k + 1 for some integer k. Substituting n into the expression Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

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