Question

If n(A) = 3,n(B)=2 then find the total number of functions from A to B
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Answer 1

Answer:

6

Step-by-step explanation:

If no of elements in set A is m and no of elements in set B is n then no of functions from A to B is m*n

Similarly here n(A) = 3

And n(B) = 2

Then no of functions from A to B is

3*2

6

Answer 2

The total number of functions from A to B = 8

Given :

n(A) = 3 , n(B) = 2

To find :

The total number of functions from A to B

Concept :

The number of relations from a set with m elements to a set with n elements $\sf = {n}^{m}$

Solution :

Step 1 of 2 :

Write down number of elements in A and B

Here it is given that n(A) = 3 , n(B) = 2

Number of elements in A = n(A) = 3

Number of elements in B = n(B) = 2

Step 2 of 2 :

Calculate total number of functions from A to B

We know that number of relations from a set with m elements to a set with n elements $\sf = {n}^{m}$

By the given , m = 3 , n = 2

Hence total number of functions from A to B

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

$= 8$

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