Let $\displaystyle P(S)$ be denoted as the power set of $\displaystyle S$ and,

Let $\displaystyle S \oplus T$ be denoted as the symmetric diference of the sets $\displaystyle S$ and $\displaystyle T$ and,

Let $\displaystyle |S|$ be denoted as the # of elements in set S.

Then, given $\displaystyle |A| = 10$ and $\displaystyle |B| = 3$,

a.) Determine the largest value possible of $\displaystyle |P(A \oplus B)|$

b.) Determine the smallest value possible of $\displaystyle |P(A \oplus B)|$

c.) Determine the largest value possible of $\displaystyle |P(A) \oplus P(B)|$

d.) Determine the smallest value possible of $\displaystyle |P(A) \oplus P(B)|$