Let R be a relation in N defined by (x, y)
Question:

Let R be a relation in N defined by (xy) ∈ R ⇔ x + 2y =8. Express R and R−1 as sets of ordered pairs.

Solution:

Let R be a relation in N defined by (xy) ∈ R ⇔ x + 2y = 8.

We have:

x = 82y

For y = 3, 2, 1, we have:

x = 2, 4, 6

∴ R = {(2, 3), (4, 2), (6, 1)}

And,

R−1  = {(3, 2), (2, 4), (1, 6)}

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