Question

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

Answer 1

The relation R from A to A is given as R = {(x, y) : 3x - y = 0, where x, y $ϵ$ A}

i.e., R = {(x, y) : 3x = y, where x, y $ϵ$ A}

$\therefore$ 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.

$\therefore$ Domain of R = {1, 2, 3, 4}

The whole set A is he codomain of the relation R.

$\therefore$ 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.

$\therefore$ Range of R = {3, 6, 9, 12}