Question

The number of surjections from A = {1, 2,...n},onto = {a, b} is

Solution

Correct option is

2n – 2

 where A has n elements and  B has 2 elements .

Each elements of A can go to 2 elements of B. Hence there will be 2. 2. 2….n times = 2n  mappings.

But if each elements of A either goes to a only of B or goes to b only of B then in these two cases the mapping will not be surjective.

Hence the number of surjective mappings is 2– 2.

SIMILAR QUESTIONS

Q1

Is equal to

Q2

Which of the following functions have inverse defined on the ranges:

Q3

 be to functions given by 

Q5

Given 

Q7

For real x, let (x) = x3 + 5x +1, then

Q8

 

 

Q9

Set A has 3 elements and set B has 4 elements. The number of injections that can be defined from to is

Q10

Let E = {1, 2, 3, 4} and F {1, 2}. Then the number of onto function fromE to F is