Let A = {2,3,5,7,9} Let R be the relation on A defined by xRy if and only if . Let l be the number of elements in R, and m be the minimum number of elements required to be added in R to make it a symmetric relatio

Question

Let A = {2,3,5,7,9} Let R be the relation on A defined by xRy if and only if $2 x \leq 3 y$ . Let $l$ be the number of elements in R, and m be the minimum number of elements required to be added in R to make it a symmetric relation. Then $l + m$ is equal to : [2026]

Smart Achievers · Accepted Answer

(1)

$A = {2, 3, 5, 7, 9}$

$y \geq \frac{2 x}{3}$

$\begin{matrix} x = 2, & y = 2, 3, 5, 7, 9 \\ x = 3, & y = 2, 3, 5, 7, 9 \\ x = 5, & y = 5, 7, 9 \\ x = 7, & y = 5, 7, 9 \\ x = 9, & y = 7, 9 \end{matrix}] \Rightarrow ℓ = 18$

To make it symmetric the elements to be added are ${(5, 2), (7, 2), (9, 2), (5, 3), (7, 3), (9, 3), (9, 5)}$

$m = 7$

$∴$ $ℓ + m = 25$

Solution

Q.
Let A = {2,3,5,7,9} Let R be the relation on A defined by xRy if and only if $2 x \leq 3 y$ . Let $l$ be the number of elements in R, and m be the minimum number of elements required to be added in R to make it a symmetric relation. Then $l + m$ is equal to : [2026]

1 25

2 23

3 27

4 21

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