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

If A is a non empty set, prove that the operation union on P(A) is a binary operation.

Let A be a non-empty set. Then a relation R on A is said to be an equivalence relation on A. If R is ______

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 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 A be a non-empty set such that AxxB=AxxC . Show that B=C .

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

Let A be a finite set . If f: A rarr A is a one-one function, show that , f is a bijection.

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

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