[Pinter 19.A.2]
Consider the ring $P_3$, the power set of $\{a,b,c\}$, with the operations given in Exercise 17.D. (namely if $A$ and $B$ are elements of $P_D$ (that is, subsets of $D$), then $A + B = (A - B) \cup (B - A)$ and $AB = A \cap B$.) The set $J = \{\emptyset, \{a\}\}$ is an ideal of $P_3$.
a. List the elements of the quotient ring $P_3/J$.
b. Construct the addition and multiplication tables of $P_3/J$.
c. Prove or disprove that $P_3/J$ a commutative ring with unity.
d. Determine whether $J$ is a maximal ideal and/or a prime ideal of $P_3$.