Question

If A={a,b,c} and B={1,2} then the number of relation from A to B is?​

Answer 1

The number of relation from A to B = 2⁶ = 64

Given :

A = { a , b , c } and B = { 1 , 2 }

To find :

The number of relation from A to B

Concept :

1. Relation :

Let S and T be two non empty sets. A binary relation R between S and T is a subset of S × T. If the ordered pair (s, t) ∈ R then the element s of the set S is said to be related to t of the set T by the relation R

2. The number of relations from a set with m elements to a set with n elements

$\sf = {2}^{mn}$

Solution :

Step 1 of 2 :

Write down number of elements in A and B

Here it is given that A = { a , b , c } and B = { 1 , 2 }

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

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

Step 2 of 2 :

Find the number of relation from A to B

We know that the number of relations from a set with m elements to a set with n elements

$\sf = {2}^{mn}$

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

So number of relations from A to B

$\displaystyle \sf{ = {2}^{(3 \times 2)} }$

$\displaystyle \sf{ = {2}^{6} }$

$\displaystyle \sf{ = 64}$

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