If A is a non-empty set and `AxxB=AxxC`, then prove that, B = C.

If A is not a null set and AxB=AxC then prove that B=C

For three sets A, B and C if A capB=AcapC andAcupB=AcupC, then prove that B = C .

If A,B,C are three non empty sets such that A cupB=A cup C and Acap B=A cap C then prove that B=C

For three sets A,B and C,if Ann C =B nn C and A uuC= B uu C , then prove that A=B

State whether the following statements is true or false : '' For two non-empty sets A and B if A subB, then AcapB=A.''

Let A, B, C be any three non-empty sets. If A uuB= A uuC, then which one of the following is denfinitely true ?

State whether each of the following statements are true or false. If the statement is false, rewrite the given statement correctly. (i) If P= {m, n} and Q = {n, m}, then P xx Q= {(m, n),(n, m)}. (ii) If A and B are non-empty sets, then A xx B is a non-empty set of ordered pairs (x, y) such that x in A and y in B. (iii) If A={1,2}, B={3,4} then A xx (B cap phi)=phi

For any two sets A and B, Prove that A cup (Acap B) = A.

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).

Use logical method to prove the following : For any two sets A and B prove that A - B = phi iff A subseteq B