" 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

If vec A, vec B and vec C are vectors such that |vec B|-|vec C| . Prove that [(vec A+ vec B)xx (vec A + vec C)]xx (vec B+vec C).(vec B+ vec C)=0

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

(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 ={2,3},B={1,2,3} and C={2,3,4} Prove that A xx A=(B xx B)nn(C xx C)

If A = {1,2,3}, B = {3,4} and C={4,5,6} Prove that A xx (B cup C) = (A xx B) cup (A xx C)

If A = {1,2,3}, B = {3,4} and C={4,5,6}, Prove that A xx (B cap C) =(A xx B) cap (A xx C)

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