The five$-$variable propositional formula

P ::$=($A$$B$$C $$D$$E $)($A $$B$$C $$E $)$

is in Disjunctive Normal Form with two $$AND$-$of$-$literal$$ clauses.

$($a$)(5$ points$)$ Find a full Disjunctive Normal Form$1$ that is equivalent to P $,$ and explain your reasoning. Hint: Can you narrow in on the important parts of the truth table without writing all of it$?$ Alternatively, can you avoid the truth table altogether?

$($b$)(5$ points$)$ Let C be a full Conjunctive Normal Form that is equivalent to P$.$ Assume that C has been simplified so that none of its $$OR$-$of$-$literals$$ clauses are equivalent to each other. How many clauses are there in C$?$ Please don$$t try to write out any of these clauses. Briefly explain your answer.