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

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

Question 14 of 35intermediate🔧 ApplyShort Answer4 marks

Let $A = \{1, 2, 3, 4, 6\}$ . Let $R$ be the relation on $A$ defined by $\{(a, b) : a, b \in A, b \text{ is exactly divisible by } a\}$ .

(i)

Write $R$ in roster form

Answer

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

(ii)

Find the domain of $R$

Answer

Domain of R = {1, 2, 3, 4, 6}

(iii)

Find the range of $R$ .

Answer

Range of R = {1, 2, 3, 4, 6}

Explanation

This question tests understanding of relations in roster form. The relation R is defined on set A where (a, b) ∈ R if b is exactly divisible by a. For each element a in A, we find all elements b in A that are divisible by a. The domain consists of all first elements of ordered pairs, and the range consists of all second elements.

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