Question

Determine the domain and range of the relation R defined by
(i) R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}

(ii) R= {(x, x3): x is a prime number less than 10}

Answer 1

(i)Given as

R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}

∴ R = {(0, 0 + 5), (1, 1 + 5), (2, 2 + 5), (3, 3 + 5), (4, 4 + 5), (5, 5 + 5)}

R = {(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}

Therefore,

The domain of relation R = {0, 1, 2, 3, 4, 5}

The range of relation R = {5, 6, 7, 8, 9, 10}

(ii) Given as

R = {(x, x3): x is a prime number less than 10}

Since, the prime numbers less than 10 are 2, 3, 5 and 7

∴ R = {(2, 23), (3, 33), (5, 53), (7, 73)}

R = {(2, 8), (3, 27), (5, 125), (7, 343)}

Therefore,

The domain of relation R = {2, 3, 5, 7}

The range of relation R = {8, 27, 125, 343}