Question

Let A = {a,b,c}and B = {5,6},find the number of relations from A to B.​

Answer 1

Step-by-step explanation:

Given:-

A = {a,b,c}and B = {5,6}

To find:-

If A = {a,b,c}and B = {5,6},find the number of

relations from A to B.

Solution:-

A={a,b,c}

Number of elements in the set A = 3

n(A)=3

B={5,6}

Number of elements in the set B= 2

n(B)=2

A x B={a,bc} x {5,6}

A × B = {(a,5),(a,6),(b,5),(b,6),(c,5),(c,6)}

n(A x B ) = 6

We know that

If n(A)=m and n(B)=n then The number of relations

from A to B = 2^(mn)

We have ,

n(A)=3

n(B)=2

The number of relations from A to B = 2^(3×2)

=>2^6

=>64

(or)

Number of relations from A to B =2^n(A×B)

=>2^6

=>64

Answer:-

The number of relations from A to B = 64

Used formulae:-

• If n(A)=m and n(B)=n then The number of relations from A to B = 2^(mn)
• Number of relations from A to B =2^n(A×B)