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*.

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

1.	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*.
Answer» 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*.