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Formula for finding number of relations is

Number of relations = 2^{ Number of elements of A × Number of elements of B }

## Where does it come from?

We know that

Relation is a subset of Cartesian product A × B

Number of relations = Number of subsets of A × B

Using Formula,

Number of subsets = 2^{ Number of elements of set }

= 2
^{
Number of elements of A × B
}

Now,

We know that

Number of elements of A × B

= Number of elements of A × Number of elements of B

Thus,

Number of relations = 2
^{
Number of elements of A × B
}

= 2
^{
Number of elements of A × Number of elements of B
}