Question

Determine the domain and range of the following relations:
(i) R = {a, b): a ∈ N, a < 5, b = 4}

(ii) S = {a, b): b = |a - 1|, a ∈ Z and |a| ≤ 3}

Answer 1

(i) Given as

R = {a, b): a ∈ N, a < 5, b = 4}

Since, the natural numbers less than 5 are 1, 2, 3 and 4

a = {1, 2, 3, 4} and b = {4}

R = {(1, 4), (2, 4), (3, 4), (4, 4)}

Therefore,

The domain of relation R = {1, 2, 3, 4}

The range of relation R = {4}

(ii) Given as

S = {a, b): b = |a - 1|, a ∈ Z and |a| ≤ 3}

Here, Z denotes integer which can be positive as well as negative

Then, |a| ≤ 3 and b = |a - 1|

∴ a = {-3, -2, -1, 0, 1, 2, 3}

For, a = -3, -2, -1, 0, 1, 2, 3 we get,

S = {(-3, |-3 – 1|), (-2, |-2 – 1|), (-1, |-1 – 1|), (0, |0 – 1|), (1, |1 – 1|), (2, |2 – 1|), (3, |3 – 1|)}

S = {(-3, |-4|), (-2, |-3|), (-1, |-2|), (0, |-1|), (1, |0|), (2, |1|), (3, |2|)}

S = {(-3, 4), (-2, 3), (-1, 2), (0, 1), (1, 0), (2, 1), (3, 2)}

b = 4, 3, 2, 1, 0, 1, 2

Therefore,

The domain of relation S = {0, -1, -2, -3, 1, 2, 3}

The range of relation S = {0, 1, 2, 3, 4}