Question

If $f:A \to B$ is a bijective function such that n(A) = 10 then n(B)

Answer 1

It is given f is a bijective function then we it is one to one and onto . For onto function every element of B is an image and for one to one the image of every element is different . Hence the number of elements of A must be equal to the number of elements of B.

Complete step-by-step answer:
We are given that f is a bijective function
A function is said to be bijective if it is one to one and onto.
So as f is onto then every element of B is a image in f
And as f is one to one , then the image of every element is different.
Therefore , this implies that the number of elements in A must be equal to the number of elements in B
And given n(A)=10
Therefore n(B)=10

Note: A bijective function or bijection is a function f : A → B that is both an injection and a surjection. This means: for every element b in the co domain B there is exactly one element a in the domain A such that f(a)=b. Another name for bijection is 1-1 correspondence.