$2.$ Prove the following conjecture using a direct proof: $($For every a$,$b is an element of integers$)(($a is even and b is odd$)>((3$a $+16-11$b$)$ is odd$)$

$3.$ Prove the following conjecture using a direct proof: $($For every a is an element of integers$)((3|$ a$)>(18|2$a$^2))$

$4.$ Prove the following conjecture using a direct proof:$($For every a$,$b is an element of integers$)(($a equivalent to $4($mod $5))>($ab equivalent to $3($mod$)5))$