Define a relation R on the set N of natural number by R
Question:

Define a relation R on the set N of natural number by R = {(xy) : y = x + 5, x is a natural number less than 4, xy ∈ N}. Depict this relationship using (i) roster form (ii) an arrow diagram. Write down the domain and range or R.

Solution:

R = {(xy) : y = x + 5, x is a natural number less than 4, xy ∈ N}

(i) ∵ x = 1, 2, 3

∴ y = 1 + 5, 2 + 5, 3 + 5

y = 6, 7, 8

Thus, we have:

R = {(1, 6), (2, 7), (3, 8)}

(ii)

Now,

Domain (R) = {1, 2, 3}

Range (R) = {6, 7, 8}

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