Let $A = {1, 2, 3, . . . ., 14}$ . Define a relation $R$ from $A$ to $A$ by $R = {(x, y) : 3 x - y = 0$ where $x, y \in A}$ . Write down its domain, co-domain and range.

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Solution

The relation $R$ from $A$ to $A$ is given as

$R = {(x, y) : 3 x - y = 0; x, y \in A}$

i.e., $R = {(x, y) : 3 x = y; x, y \in A}$

$∴ R = {(1, 3), (2, 6), (3, 9), (4, 12)}$

The domain of $R$ is the set of all first elements of the ordered pairs in the relation

$∴$ Domain of $R = {1, 2, 3, 4}$

The whole set $A$ is the co-domain of the relation $R$

$∴$ Codomain of $R = A = {1, 2, 3, . . . . ., 14}$

The range of $R$ is the set of all second elements of the ordered pairs in the relation.

$∴$ Range of $R = {3, 6, 9, 12}$

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