Let A and B be two sets each with a finite number of elements. Assume that there is an injective mapping from A to Band that there is an injective mapping from B to A Prove that there is a bijective mapping from A to B.

Let A and B be two finite sets, then the number of functions from A to B is

Let A and B be two finite sets having m and n elements respectively. Then the total number of mappings from A to B is

Let A and B be two finite sets having m and n elements respectively. Then the total number of mappings from A to B is

If A and B are two sets such that n(A)=5 and n(B) = 6, then the number of one-one and onto mapping from A to B is

Given, A = {2,3,4}, B={2,5,6,7} . Construct an example of each of the following (i) an injective mapping from A to B. (ii) a mapping from A to B which is not injective. (iii) a mapping from B to A.

Let A and B be two sets. Show that f: AxxB->BxxA defined by f(a ,\ b)=(b ,\ a) is a bijection.

Let A and B be two sets. Show that f: AxxB->BxxA defined by f(a ,\ b)=(b ,\ a) is a bijection.

Let A and B be two finite sets having m and n elements respectively such that m le n . A mapping is selected at random from the set of all mappings from A to B. The probability that the mapping selected is an injection, is

Let A and B be two finite sets having m and n elements respectively such that m≤n . A mapping is selected at random from the set of all mappings from A to B. The probability that the mapping selected is an injection, is In above question if m gt n then the probability that the mapping selected is an injective mapping is :

Let A be a finite set containing 3 elements, then the number of functions from A to A is