Determine the domain and range of the relation R defined by

Question:

Determine the domain and range of the relation R defined by

(i) R = [(xx + 5): x ∈ (0, 1, 2, 3, 4, 5)]

(ii) R = {(xx3) : x is a prime number less than 10}

Solution:

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

We have:

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

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

∴ Domain (R) = {0, 1, 2, 3, 4, 5}

Range (R) = {5, 6, 7, 8, 9, 10}

(ii) R = {(xx3) : x is a prime number less than 10}

We have:

x = 2, 3, 5, 7

x3  = 8, 27, 125, 343

Thus, we get:

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

Domain (R) = {2, 3, 5, 7}

Range (R) = {8, 27, 125, 343}

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