Let $X$ be a non-empty set and let * be a binary operation on $P\left(X\right)$ (the power set of set $X)$ defined by $A\cdot B=A\cup B$ for all $A,B\in P\left(X\right)$ . Prove that * is both commutative and associative on $P\left(X\right)$ . Find the identity element with respect to * on $P\left(X\right)$ . Also, show that $\phi \in P\left(X\right)$ is the only invertible element of $P\left(X\right)\dot{}$

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