Question

Write down the contrapositive of the statement “If 3n2 + 4 is even then n is even.” Then prove the statement for all integers n.

Answer 1

Answer on Question #76362 – Math – Discrete Mathematics

Question

Write down the contrapositive of the statement "If $3n^2 + 4$ is even then $n$ is even." Then prove the statement for all integers $n$.

Solution

Contrapositive of this statement is "If $n$ is odd then $3n^2 + 4$ is odd."

Proof of the initial statement (proof of the contrapositive statement follows from it).

$$3n^2 + 4 \mathbin{\text{:}} 2 \Rightarrow 3n^2 \mathbin{\text{:}} 2 \Rightarrow n \mathbin{\text{:}} 2, QED.$$

Answer:

"If $n$ is odd then $3n^2 + 4$ is odd."

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