# Q. 9 Given a non-empty set X, consider the binary operation given by , 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      is defined as  .

As we know that

Hence, X is the identity element of binary operation *.

Now, an element  is invertible if there exists a  ,

such that              (X is identity element)

i.e.

This is possible only if  .

Hence, X is only invertible element  in  with respect to operation *

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