Q. 1

Let A and B be two nonempty sets.

(i) What do you mean by a relation from A to B?

(ii) What do you mean by the domain and range of a relation?

Answer :

(i) If A and B are two nonempty sets, then any subset of the set (A × B) is said to a relation R from set A to set B.


That means, if R be a relation from A to B then R (A × B).


Therefore, (x, y) R (x, y) (A × B)


That means x is in relation to y. Or we can write xRy.


(ii) Let R be a relation from A to B. Then, the set containing all the first elements of the ordered pairs belonging to R is called Domain.


For the relation R, Dom(R) = {x: (x, y) R}


And the set containing all the second elements of the ordered pair belonging to R is called Range.


For the relation R, Range(R) = {y: (x, y) R}


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