Use the definition of O$,\backslash$Omega and $\backslash$Theta $,$ to prove the following; do not use limits$.$ In your solution, give sufficient details to carefully argue why the constants that you have chosen guarantee that the inequality holds in the definition of order notation.

$($a$)3$n$2+1/$lgn in O$($n$2).($b$)1/5$n$35$n$2$ in $\backslash$Omega $($n$3).$