Given a non-empty set X, consider the binary operation : P(X) × P(X) → P(X) given by A B = A ∩ B &mnForE; A, B in 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*.

Asked by I T Roxaana 04/09/2019 Last Modified 18/09/2019

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Given a non-empty set X, consider the binary operation *: P(X) × P(X) → P(X) given by A * B = A ∩ B &mnForE; A, B in 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*.

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Given a non-empty set X, consider the binary operation : P(X) × P(X) → P(X) given by A B = A ∩ B &mnForE; A, B in 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*.