Question

Total number of relations from a set consisting of m elements to a set consisting or n element is …​

Answer 1

Answer:

total number of relations from a set containing n elements is 2ⁿ² .

for example

if a set has 3 elements then it has

2³^² relations

that is 2⁶ = 64 relations.

Answer 2

Total number of relations from a set consisting of m elements to a set consisting or n element is ${2}^{mn}$

Given: A set consisting of m elements to a set consisting or n element

To Find: Total number of relations

Solution:

Let A and B be finite sets containing m and n elements respectively

O(A)=m and O(B)=n.

Hence O(A×B)=mn

Since every subset of A×B is a relation from A to B, therefore, number of relations from A to B is equal to the number of the subsets of A×B, i.e., ${2}^{mn}$

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