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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}
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}
Determine the domain and range of the following relations:
(i) {(–3, 1), (–1, 1), (1, 0), (3, 0)}
(ii) {(x, y): x is a multiple of 3 and y is a multiple of 5}
(iii) {(x, x2): x is a prime number less than 15}
Determine the domain and range of the following relations:
(i) {(–3, 1), (–1, 1), (1, 0), (3, 0)}
(ii) {(x, y): x is a multiple of 3 and y is a multiple of 5}
(iii) {(x, x2): x is a prime number less than 15}
(i) Domain = {–3, –1, 1, 3}, Range = {0, 1}
(ii) Domain = {x : x is a multiple of 3} = {3n : n ∈ Z}
Range = {y : y is a multiple of 5} = {5n : n ∈ Z}
(iii) Relation = {(x, x2) : x is a prime number less than 15}
= {(2, 4), (3, 9), (5, 25), (7, 49), (11, 121), (13, 169)}
Domain = {2, 3, 5, 7, 11, 13}, Range = {4, 9, 25, 49, 121, 169}
(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}