(Solved): 7. Let denote the binary operation for XOR (exclusive-or) given by the truth table below: (a) ...

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).