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7. Let $?$ denote the binary operation for XOR (exclusive-or) given by the truth table below: (a) Use truth tables to find $P?P$ and $P?F$. (b) Recall that a binary operation $?$ is called commutative if $P?Q=Q?P,$ for all $P,Q$. Is $?$ commutative? Justify your answer. (c) Recall that a binary operation is called associative if $(P?Q)?R=P?(Q?R),$ for all $P,Q,R$. Is $?$ associative? Justify your answer. (Hint: try truth tables) (d) Without using truth tables, simplify $(P?Q)?P$. (Hint: Use parts a-c).