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)
This is possible only if .
Hence, X is only invertible element in with respect to operation *