Given non-empty set X, consider the binary operation ∗:P(X)×P(X)→P(X) given by A∗B=A∩B∀A,B in P(X), where P(X)is the power set of X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation.

Given non-empty set X, consider the binary operation ∗:P(X)×P(X)→

1.	Given non-empty set X, consider the binary operation ∗:P(X)×P(X)→P(X) given by A∗B=A∩B∀A,B in P(X), where P(X)is the power set of X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation.
Answer» Given non-empty set X, consider the binary operation $* : P (X) \times P (X) \to P (X)$ given by $A * B = A \cap B \forall A, B$ in P(X), where P(X)is the power set of X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation.