Question

If total number of relations from A to B is 64 and
from B to C is 16, then the sum of possible values of
n(B) is .......​

Answer 1

Answer:

Step-by-step explanation:

For any set A such that n(A)=n

then number of all relations on A is 2  

n  

2

 

 

As the total number of Relations that can be defined from a set A to B is the number of possible subsets of A×B. If n(A)=p and n(B)=q then n(A×B)=pq and the number of subsets of A×B = 2  

pq

.The number of relations between sets can be calculated using 2  

mn

 where m and n represent  

the number of members in each set.

Given that n(A)=2 and n(B)=m

So,  

2  

2m

=64

2  

2m

=2  

6

 

On comparing powers of 2 we get,

2m=6

m=3