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.

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

Let P(A) be the power set of a non-empty set A. Prove that union (cup) and intersection (cap) of two subsets X and Y of A are binary operations on P(A).

If P and Q are any two set then P-Q=

Let P(A) be the power set of a non-empty set A and a binary operation @ on P(A) is defined by X@Y=XcupY for all YinP(A). Prove that, the binary operation @ is commutative as well as associative on P(A). Find the identity element w.r.t. binary operation @ on P(A). Also prove that Phi inP(A) is the only invertible element in P(A).

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.

Given P(A) = 3/5 and P(B) = 1/5 . Find P(A or B) , if A and B are mutually excluive events.

For any two events A and B, show that, P(A uu B) = P(A) + P(B) - P(A nn B) .

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

Prove that P(A uu B) = P(A) + P(B) - P(A nn B)

Let S be a non-empty set and P(S) be the power set of the Set S. Statement -I: Phi is the identity element for union as a binary operation on P(S) Statement -II: S is the identity element for intersection on P(S).