If a relation R is defined from a set A = {2, 3, 4, 5} to a set B = {3, 6, 7, 10} as follows (x, y) ? R ? x divides y. Expression of R?¹ is represented by

Question

If a relation R is defined from a set A = {2, 3, 4, 5} to a set B = {3, 6, 7, 10} as follows $(x, y) \in R \Leftrightarrow x$ divides $y$ . Expression of $R^{- 1}$ is represented by

Smart Achievers · Accepted Answer

(3)

Recall that $a ∣ b$ stands for $a$ divides $b$ . For the elements of the given sets $y$ and $R^{- 1}$ , we find $2 ∣ 6, 2 ∣ 10, 3 ∣ 3, 3 ∣ 6, 5 ∣ 10$

$\Rightarrow$ $R = {(2, 6), (2, 10), (3, 3), (3, 6), (5, 10)}$

$∴$ $R^{- 1} = {(6, 2), (10, 2), (3, 3), (6, 3), (10, 5)}$

Solution

Q.
If a relation R is defined from a set A = {2, 3, 4, 5} to a set B = {3, 6, 7, 10} as follows $(x, y) \in R \Leftrightarrow x$ divides $y$ . Expression of $R^{- 1}$ is represented by

1 {(6, 2), (10, 2), (3, 3), (6, 3)}

2 {(6, 2), (3, 3), (10, 5), (10, 2)}

3 {(6, 2), (10, 2), (3, 3), (6, 3), (10, 5)}

4 None of these

Ans.
(3)

Recall that $a ∣ b$ stands for $a$ divides $b$ . For the elements of the given sets $A$ and $B$ , we find $2 ∣ 6, 2 ∣ 10, 3 ∣ 3, 3 ∣ 6, 5 ∣ 10$

$\Rightarrow$ $R = {(2, 6), (2, 10), (3, 3), (3, 6), (5, 10)}$

$∴$ $R^{- 1} = {(6, 2), (10, 2), (3, 3), (6, 3), (10, 5)}$

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