Proving biconditional statements

To prove that a biconditional statement of the form p$$ q is true, you must prove that p$->$ q and p$->$ q are both true. For example, to prove that for any integer n$,$ n is odd if and only if n$^2$ is odd, you must prove that $(1)$ if n is odd, then n$^2$ is odd, and $(2)$ if n$^$ is odd, then n is odd.

$($a$)$ Prove that for any integer n$,$ n is odd if and only if $5$n$+3$ is even. Indicate which

proof methods you used, as well as the assumptions $($what you suppose$)$ and the

conclusions $($what you need to show$)$ of the proof.