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 $\mathrm{R} \subset \mathrm{R}{1}$ and the number of elements in $\mathrm{R}{1}$ is $\mathrm{n}$. Then, the minimum value of $n$ is
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Answer (66)
Solution
$\mathrm{R}={(3,2),(6,4),(9,6),(12,8), \ldots \ldots .(99,66)}$
$\mathrm{n}(\mathrm{R})=33$
$\therefore 66$
