Question:
Define a relation R on the set N of natural number by R = {(x, y) : y = x + 5, x is a natural number less than 4, x, y ∈ N}. Depict this relationship using (i) roster form (ii) an arrow diagram. Write down the domain and range or R.
Solution:
R = {(x, y) : y = x + 5, x is a natural number less than 4, x, y ∈ 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)
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Now,
Domain (R) = {1, 2, 3}
Range (R) = {6, 7, 8}