If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is

Question

Philoid · Accepted Answer

Number of elements in A = 5

Number of elements in B = 6

Now, for a function to be one-one all elements of domain should have unique image in co-domain.

Here, 5 elements of A can be mapped to 5 distinct element of B.

⇒ function is one-one

But range of B is 6 that means there is one element in B which does not have pre-image in A.

Thus the function cannot be onto if it is one-one.

Also, if all 6 elements of B are mapped to all 5 elements of A, then we can observe there will be atleast 2 elements of B which have same pre-image in A.

⇒ one element of A will have two image in B.

⇒ function is not one-one

Thus the function cannot be one-one if it is onto.

Hence, there cannot be any one-one and onto mapping from A to B.