If `X= A nn B` then prove that `X xx X = (A xx A) nn (B xx B)`

(i) If A sube B , prove that A xx A sube (A xx B) nn (B xx A) (ii) If A sube B , prove that A xx C sube B xx C for any set C.

If A nn C=phi, then prove that (A xx B)nn(C xx B)=phi

If A sube B then prove that (A xx B)nn(B xx A)=A^(2)

If A= {1, 2, 3}, B= {4},C = {5}. then verify that : A xx (B nn C)= (A xxB) nn (A xx C) .

Theorem 1 (ii) (For any three set A;B;C ; prove that A xx(B nn C)=(A xx B)nn(A xx C)

For any three sets A, B, C, prove that : Axx(B nn C)=(A xx B)nn (Axx C) .

Theorem 8( For any set A;B and C prove that A xx(B'uu C')'=(A xx B)nn(A xx C)

For any three sets A, B,C prove that : (A nn B) xx C= (AxxC) nn (BxxC) .

Prove that : (A-B) nn (A nn B)=phi .

For any four sets A, B, C and D, prove that : (A nn B)xx (C nn D)= (AxxC) nn (BxxD) .