Q. 13 Given a non-empty set X, let be defined as
Show that the empty set is the
identity for the operation ∗ and all the elements A of P(X) are invertible with
. (Hint : and ).
Let be defined as
Let . Then
Thus, is identity element for operation *.
An element will be invertible if there exists ,
such that . (here is identity element)
Hence, all elements A of P(X) are invertible with