Sets, Relations & Functions
Relation — l+m+n (Count, Reflexive, Symmetric)
nta_pyq_2026_jan
Grade None
Question:
Let $A=\{-2,-1,0,1,2,3,4\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $2x+y\leq2$. Let $l$ be the number of elements in $R$. Let $m$ and $n$ be the minimum number of elements required to be added in $R$ to make it reflexive and symmetric respectively. Then $l+m+n$ is equal to:
Step-by-Step Solution
Key Concept: Count $(x,y)$ with $2x+y\leq2$: $x=-2$: all 7, $x=-1$: all 7, $x=0$: 5, $x=1$: 3, $x=2$: 1, $x=3,4$: 0. $l=23$.
$l+m+n=33$.
Correct Answer: 3