Let A and B sets. Show that `f : A xx B to Bxx A ` such that `f (a,b) = (b,a) ` is bijective function.

If f : A rarr B is surjective then

For any sets A and B, show that P ( A ∩ B ) = P ( A ) ∩ P ( B ) .

Let A, B, and C be the sets such that A ∪ B = A ∪ C and A ∩ B = A ∩ C . Show that B = C .

Let A and B be two non- empty subsets of a set X such that A is not a subset of B .Then

Let f: A rarr B and g : B rarr C be the bijective funtions. Then (gof)^-1 is

Show that if f: A to B and g: B to C are onto, then gof : A to C is also onto.

Let A and B be two sets such that n(A) =3 and n(B) =2. If (x, 1), (y, 2), (z,1) are in A xx B, find A and B, where x, y and z are distinct elements.

Show that if f : A to B and g: B to C are one-one, then gof: A to C is also one-one.