" - 7.Prove that "A times B=B times A rArr A=B" ."

Let A and B be sets.Show that f:A times B rarr B times A such that (a,b)=(b,a) is bijective function.

Evaluate : b times b times b times b

Prove that (A uu B)xx C=(A xx C)uu(B xx C)

Express the following in exponential form: (i) "6 times 6times6 times 6 (ii) t times t (iii) b times b times b times b times b times b (iv) 5 times 5times7 times 7times7 (v) "2 times 2times a times a (vi) a times a times a times c times c times c times c times d times 1

(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.

For any three sets A, B, C . prove that A xx (B cup C)=" (A xx B) cup(A xx C)

If A sube B, prove that A xx C sube B xx C for any set C.

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

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

If A = {1,2,3}, B = {3,4} and Prove that A xx B not= B xx A