Theorem 9(A and B are two non empty set having n element in common ; then prove that `AxxB` and `BxxA` have `n^2` element in common.)

Sets A and B have n elements in common. How many elements will (AxxB) and (BxxA) have in common?

A and B are two sets having 3 elements in common. If n(A)=5, n(B)=4, then what is n(AxxB) equal to ?

Two sets having no element in common are called "_____" sets.

If P and Q are sets having 5 elements in com-mon, then how many elements do P xx Q and Q xx P have in common ?

If A and B are two non-empty sets having n elements in common,then what is the number of common elements in the sets A xx B and B xx A?

Sets A and B have n element in common. How many elements will (A xx B) and (B xx A) have in common?

Let A and B be two sets having 3 elements in common. If n (A) = 5 and n (B) = 4 , then n((AxxB)nn(BxxA)) =