Exercise $6\mathrm{.}1.$ let a$,$ b$,$ and c be integers. Prove each of the following statements.

$($a$)$ If a

$2$

is odd, then a is odd.

$($b$)$ If a and b are even, then a $+$ b is even.

$($c$)$ If a divides b $1$ and a divides c $1,$ then a divides bc $1.$