Use Definition $3\mathrm{.}1$ for even numbers and Definition $3\mathrm{.}4$ for odd numbers to justify your answers for $($a$)($c$).$ Assume that c is a particular integer.

$($b$)$

Is

$6$c $+3$

an even or an odd integer?

Odd, because $6$c $+3=2(3$c $+1)+1$ and $3$c $+1$ is an integer.Even, because $6$c $+3=2(3$c $+1)$ and $3$c $+1$ is an integer. $$Odd$,$ because $6$c $+3=2(3$c $+1)$ and $3$c $+1$ is an integer.Even, because $6$c $+3=2(3$c $+1)+1$ and $3$c $+1$ is an integer.

$($c$)$

Is

$($c$2+3)($c$23)6$

an even or an odd integer?

Odd, because $($c$2+3)($c$23)6=2(0)+1$ and $0$ is an integer.Even, because $($c$2+3)($c$23)6=2(0)$ and $0$ is an integer.$$Odd$,$ because $($c$2+3)($c$23)6=2(0)$ and $0$ is an integer.Even, because $($c$2+3)($c$23)6=2(0)+1$ and $0$ is an integer.