Question

If a set A has 3 elements and B has 2 elements, then the number of functions from B to A is ……..

Answer 1

There are,

2 (3X2) relations from Set A to B.

2^6=64 relation between A and B.

Answer 2

The number of functions from B to A is 9

Given :

Set A has 3 elements and B has 2 elements

To find :

The number of functions from B to A

Concept :

If a set A has n elements and set B has m elements, then the number of functions possible from A to B is mⁿ

Solution :

Step 1 of 2 :

Write number of elements in A and B

Number of elements in A = 3

Number of elements in B = 2

Step 2 of 2 :

Calculate number of functions from B to A

We know that if a set A has n elements and set B has m elements, then the number of functions possible from A to B is mⁿ

Hence the number of functions from B to A

$\displaystyle \sf = {3}^{2}$

$\displaystyle \sf = 9$

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