Q$4(10$ points$)$

Let $P$ be a boolean formula in variables $p$ and $q,$ of any length, using any of the logical operators not,${?}^{{?}^{?}},v,=>,>.$ For example, $P$ could be $)>((qvvnotp).$ Prove that $P$ is logically equivalent to a formula of the form

$AB$

where $$ is one of ${?}^{{?}^{?}},vv,>,$ and A and $B$ are chosen from $\{p,$notp,$q,$notq$\}.$

Note: you do not need to find an "elegant" proof of this.

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