Let $A=\{1,2,3\}, B=\{1,2,3,4\}$ and $C=\{1,2,3,4,5\}$. For the sets $S$ and $T$ described below, explain whether $|S|<|T|,|S|\rangle|T|$ or $|S|=|T|$.
(a) Let $B$ be the universal set and let $S$ be the set all subsets $X$ of $B$ for which $|X| \neq|\bar{X}|$. Let $T$ be the set of 2-element subsets of $C$.
(b) Let $S$ be the set of all partitions of the set $A$ and let $T$ be the set of 4-element subsets of $C$.
(c) Let $S=\{(b, a): b \in B, a \in A, a+b$ is odd $\}$ and let $T$ be the set of all nonempty proper subsets of $A$.