$10\mathrm{.}7.$ In this problem you will show that putting a formula into conjunctive

normal form may increase its length exponentially. Consider the formula

p$1$ q$1...$ pn $$ qn$,$

where n $>=1$ and the pi and qi are propositional variables. This formula has

length $4$n $1,$ if we count each occurrence of a propositional variable or an

operator as adding $1$ to the length and ignore the implicit parentheses.

$($a$)$ Write out a conjunctive normal form of this formula in the case n $=3$