Question

Differentiate between the Relation and Function. If 64 relations are there
from the set A to set B then how many possible number of elements are
there in set A and set B. | || Class 11

Answer 1

Answer:

$\huge\textbf{❥ᴀ᭄ɴsᴡᴇʀ}$

• If set A has m elements and set B has n elements, then there are 2^(mn) relations between A and B. Hence, there are 2^ (3*2) relations from set A to set B i.e. there are 2^(6) = 64 relations between A and B.

$\huge\purple\sf{\fbox{\fbox \purple{➳ᴹᴿ᭄ \: ąཞყąŋ}}}$

Answer 2

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

then number of all relations on A is 2 n²

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 .