Let A and B be two nonempty sets. (i) What do you mean by a relation

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}

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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