To find no. of surjective function.

Question

Let A={1,2,3,4,.........,n} and B={a,b}.Then the number of surjective functions from A to B is

(a) ^nP₂                      (b)2ⁿ-2         (c)2ⁿ-1         (d)NOT

Answer 1

A={1,2,3,......n}  B={a,b}

A has n elements B has 2 elements

number of surjection is 2ⁿ−2

So, option (b) is correct

Note: The number of surjections from set A having n elements to set B having 2 elements is 2ⁿ−2