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```					3/20/2011                                  NCERT CBSE Math Solutions for Class XI…

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Question 9:

Given a 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)
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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It is given that                                                                     .

We know that                                   .

Thus, X is the identity element for the given binary operation *.

Now, an element            is invertible if there exists            such that

This case is possible only when A = X = B.

Thus, X is the only invertible element in P(X) with respect to the given operation*.

Hence, the given result is proved.

…meritnation.com/…/C@WFkOyiJG6Qxt…                                                                                             1/1

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