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Relation

A relation R from a non-empty set A to another non-empty set B is a subset of A × B. Equivalently, any subset of A × B is a relation from A to B.
 
Thus, R is a relation from A to B R A × B R {(a, b) : a A, b B}.
 
Here A is called its domain and B is called its codomain.
 
Let R be a relation from A to B.
 
The range of R is the set of all those elements b B such that (a, b) R for some a A, range of R = set of second components of all the ordered pairs which belong to R.

Total number of relations

Let A and B be two non-empty finite sets having p and q elements respectively. Then n (A × B) = n(A) × n(B) = pq. Therefore, total number of subsets of A × B = 2pq.
 
Since each subset of A × B is a relation from A to B, therefore total number of relations from A to B is 2pq.




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