considering India as the universal set. write the relation between the state and capital of India in the form of subset
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Let the number of elements of the sets A and B be p and q respectively. Then the number of relations from the set A to the set B is
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Given A and B are two sets with number of elements p and q respectively.
The cartesian product of A and B=A×B={(a,b):(a∈A) and (b∈B)}
Number of elements in A×B=∣A×B∣=∣A∣.∣B∣=pq
Any relation from A to B is a subset of A×B.
Hence number of relations from A to B is the number of subsets of A×B
=2
∣A×B∣
=2
pq
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