Let A = 1, 2, 3, 4, 5, 6 . Let R be a relation on A defined by (a, b) : a, b ∈ A, b is exactly divisible by a 1. Writer R in roster form. 2. Find the domain of R. 3. Find the range of R.

We have, A = 1, 2, 3, 4, 5, 6 and, (a, b): a, b ∈ A, b is exactly divisible by a 1. Now, a b stands for 'a divides b'. For the elements of the given sets A and A, we find that, 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 Relation R in roster form is 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) 2. Domain(R) = 1, 2, 3, 4, 5, 6 3. Range(R) = 1, 2, 3, 4, 5, 6

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

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Question

Let A = {1, 2, 3, 4, 5, 6}. Let R be a relation on A defined by
{(a, b) : a, b ∈ A, b is exactly divisible by a}

Writer R in roster form.
Find the domain of R.
Find the range of R.

✓

Answer

We have,
A = {1, 2, 3, 4, 5, 6}
and, {(a, b): a, b ∈ A, b is exactly divisible by a}

Now, $\frac{\text{a}}{\text{b}}$ stands for 'a divides b'. For the elements of the given sets A and A, we find that,

$\frac{1}{1},\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\frac{1}{6},\frac{2}{2},\frac{2}{4},\frac{2}{6},\frac{3}{3},\frac{3}{6},\frac{4}{4},\frac{5}{5},\frac{6}{6}$

$\therefore$ Relation R in roster form is

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)}

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

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