Let A = [1, 2, 3, 4, 5, 6]. Let R be a relation on A defined by

Question:

Let A = [1, 2, 3, 4, 5, 6]. Let R be a relation on A defined by

{(ab) : ab ∈ A, b is exactly divisible by a}

(i) Writer R in roster form

(ii) Find the domain of R

(ii) Find the range of R.

Solution:

A = [1, 2, 3, 4, 5, 6]

R = {(ab) : ab ∈ A, b is exactly divisible by a}

(i) Here,

2 is divisible by 1 and 2.

3 is divisible by 1 and 3.

4 is divisible by 1 and 4.

5 is divisible by 1 and 5.

6 is divisible by 1, 2, 3 and 6.

∴ R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (5, 5), (6, 6)}

(ii) Domain (R) = {1, 2, 3, 4, 5, 6}

(iii) Range (R) = {1, 2, 3, 4, 5, 6}

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