Set, Relation and FunctionMedium
Question
Let $A = \{ 2,3,5,7,9\}$. Let R be the relation on A defined by x Ry if and only if $2x \leq 3y$. Let $\mathcal{l}$ 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 $\mathcal{l} + m$ is equal to:
Options
A.23
B.25
C.21
D.27
Solution
$\ A = \{ 2,3,5,7,9\}$
$$\left. \ \begin{matrix} & y \geq \frac{2x}{3} \\ x = 2, & y = 2,3,5,7,9 \\ x = 3, & y = 2,3,5,7,9 \\ x = 5, & y = 5,7,9 \\ x = 7, & y = 5,7,9 \\ x = 9 & y = 7,9 \end{matrix} \right\rbrack \rightarrow \mathcal{l} = 18 $$to make it symmetric elements to be added are
$${\{(5,2),(7,2),(9,2),(5,3),(7,3),(9,3),(9,5)\} }{m = 7 }{\therefore\ \mathcal{l} + m = 25}$$
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