Sets, Relations & Functions
Relation on Set — l+m (Elements and Symmetry)
nta_pyq_2026_jan
Grade 11
Question:
Let $A=\{2,3,5,7,9\}$. Let $R$ be the relation on $A$ defined by $xRy$ if and only if $2x\leq3y$. 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:
Step-by-Step Solution
Key Concept: $xRy\Leftrightarrow y\geq2x/3$. For each $x\in A$, count valid $y$: $x=2$: 5 pairs, $x=3$: 5, $x=5$: 3, $x=7$: 3, $x=9$: 2. $l=18$.
$l=18$, $m=7$. $l+m=25$.
Correct Answer: 4