### Sets And Relations Question 10

#### Question 10 - 2024 (31 Jan Shift 2)

Let $A={1,2,3, \ldots \ldots, 100}$. Let $R$ be a relation on $A$ defined by $(x, y) \in R$ if and only if $2 x=3 y$. Let $R _1$ be a symmetric relation on $A$ such that $R \subset R _1$ and the number of elements in $R _1$ is $n$. Then, the minimum value of $n$ is

## Show Answer

#### Answer (66)

#### Solution

$R={(3,2),(6,4),(9,6),(12,8), \ldots \ldots .(99,66)}$

$n(R)=33$

$\therefore 66$