A relation R is defined from a set A = [2, 3, 4, 5] to a set B = [3, 6, 7, 10] as follows:
Question:

A relation R is defined from a set A = [2, 3, 4, 5] to a set B = [3, 6, 7, 10] as follows:

(xy) ∈ R ⇔ x is relatively prime to y

Express R as a set of ordered pairs and determine its domain and range.

Solution:

Given:

(xy) ∈ R ⇔ x is relatively prime to y.

Here,

2 is co-prime to 3 and 7.

3 is co-prime to 7 and 10.

4 is co-prime to 3 and 7.

5 is co-prime to 3, 6 and 7.

Thus, we get:

R = {(2, 3), (2, 7), (3, 7), (3, 10), (4, 3), (4, 7), (5, 3), (5, 6), (5, 7)}

Domain of R = {2, 3, 4, 5}

Range of R = {3, 7, 6, 10}

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