FINDING DOMAIN AND RANGE OF A RELATION

Domain, Codomain and Range of a Relation

• The domain of the relation R ={x ∈ A | x R y, for some y ∈ B}
• The co-domain of the relation R is B.
• The range of the relation R ={y ∈ B | x R y, for some x ∈ A}
• From these definitions, we note that domain of R ⊆A, co-domain of R = B and range of R ⊆ B.

Solved Questions

Question 1 :

Let A = {1, 2, 3, 4,..., 45} and R be the relation defined as “is square of ” on A. Write R as a subset of A x A. Also, find the domain and range of R.

Solution :

A = {1, 2, 3, 4,..., 45}

Let "A" be a set which contains some of elements of A

A = {1, 2, 3, 4, 5, 6}

Now, we have to write the other set of elements from A. The elements in this set denotes the square value of previous set.

Square values of set A  =  {1, 4, 9, 16, 25, 36}

A x A  =  {(1, 1)(1,4)(1, 9)(1, 16) (1, 25)  (1, 36)..................}

Domain  =  {1, 2, 3, 4, 5, 6}

Range  =  {1, 4, 9, 16, 25, 36}

Question 2 :

A Relation R is given by the set {(x, y) /y = x + 3, x ∈  {0, 1, 2, 3, 4, 5}}. Determine its domain and range.

Solution :

Given that :

y  =  x + 3

R  =  {(0, 3) (1, 4) (2, 5) (3, 6) (4, 7) (5, 8)}

Domain of R  =  {0, 1, 2, 3, 4, 5}

Range of R  =  {3, 4, 5, 6, 7, 8}

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