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

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Solution

Q.
Let A = {1, 2, 3, ..........., 100}. Let R be a relation on A defined by (x, y) ∈ R if and only if 2x = 3y. 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 ______. [2024]

Ans.
(66)

We have, A = {1, 2, 3, ..., 100}

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

n(R) = 33

Since, $R_{1}$ is symmetric and $R \subset R_{1}$

∴ n( $R_{1}$ ) = 66

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