$($a$)$ Consider a compound predicate $S$ consisting of two constituent predicates $P$ and $Q.$ The

predicate $S$ returns true precisely when an even number of its constituent predicates are

true. Using only the classical operations of AND ${(}^{{?}^{?}}),$ OR $(vv),$ and NOT $(not),$ construct

$S.$ Use a truth$-$table to verify that your answer is correct.

$($b$)$ Now consider the case of a compound predicate $U$ which consists of three constituent

predicates $P,Q,$ and $R,$ and returns true precisely when an even number of its con$-$

stituent predicates are true. Let $S$ be the compound predicate you constructed in part

$($a$).$ Using only the predicates $R$ and $S,$ and the classical operations of AND $({?}^{{?}^{?}}),$ OR

$(V),$ and NOT $(not),$ construct $U.$ Use a truth$-$table to verify that your answer is correct.

PLEASE ANSWER A & B$,$