Let P

be a boolean formula in variables p

and q

$,$ of any length, using any of the logical operators $,,,,$

$.$ For example, P

could be $($p$($q$$p$))$

$.$ Prove that P

is logically equivalent to a formula of the form

A$\backslash$geoquad B

where $\backslash$geoquad

is one of $,,$

$,$ and A

and B

are chosen from $\{$p$,$p$,$q$,$q$\}$

$.$

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