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in Sets, Relations and Functions by (44.7k points)
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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?

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(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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