Exercise 5.
Prove that for all integers \(n\text{,}\) it is the case that \(n\) is even if and only if \(3n\) is even. That is, prove both implications: if \(n\) is even, then \(3n\) is even, and if \(3n\) is even, then \(n\) is even.
Prove that for all integers \(n\text{,}\) it is the case that \(n\) is even if and only if \(3n\) is even. That is, prove both implications: if \(n\) is even, then \(3n\) is even, and if \(3n\) is even, then \(n\) is even.