Let A be any non-empty set. Then, prove that the identity function on set A is a bijection.

Define empty set .

Let A be a non-empty set and S be the set of all functions from A to itself. Prove that the composition of functions 'o' is a non-commutative binary operation on Sdot Also, prove that 'o' is an associative binary operation on Sdot

Let X be any non-empty set containing n elements, then the number of relations on X is

Let A be a non-empty set such that A xx B=A xx C. Show that B=C

Let S be a non-empty set and P(s) be the power set of set S.Find the identity element for all union () as a binary operation on P(S).

If Aa n dB are any two non-empty sets, then prove that: AxxB=BxxA A=Bdot

Let X be a non-empty set and let * be a binary operation on P(X)( the power set of set X) defined by A*B=(A-B)uu(B-A) for all A,B in P(X) .Show that varphi is the identity element for * on P(X) .

Let X be any non-empty set containing n elements. Then what is the number of relations on X ?

Let A, B, C and D be four non-empty sets. The contrapositive statement of ''If A sube B and B sube D , then A sube C '' is :