Let P be the set of all subsets of a given set X. Show that `uu:P xx P to P ` given by ` (A,B) to A uuB and nn:PxxP to P` given by `(A,B) to A nnB` are binary operations on the set P.

Let A and B be two non- empty subsets of a set X such that A is not a subset of B .Then

For any sets A and B, show that P ( A ∩ B ) = P ( A ) ∩ P ( B ) .

If P is the set of all parallelograms and T is the set of all trapeziums then P nn T is

The relation 'is subset of' on the power set P(A) of a set A is :

Given a non empty set X, consider P (X) which is the set of all subsets of X. Define the relation R in P(X) as follows : For subsets A, B in P(X), ARB if and only if A sub B. Is R an equivalence relation on P (X)? Justify your answer.

Assume that P ( A ) = P ( B ) . Show that A = B

If P={1,2}, form the set P xx P xx P