Let A=\ -3,-2,-1,0,1,2,3\ and R be a relation on A defined by x R y if and only if 2 x-y ∈\ 0,1\ . 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

Correct answer: B. 17 aligned & array l 2 x-y=0 \ 0,0\ \ -1,-2\ \ 1,2\ 2 x-y=1 array & \ 0,-1\ \ 1,1\ \ 2,3\ \ -1,-3\ & Total (0,0)(-1,-2),(1,2)(0,-1),(1,1)(2,3)(-1,-3) & Reflexive m=5 & =7 & Symm. n=5 +m+n=17 & option (2) aligned

JEE Main 20254 AprilEvening Shift

Exam: JEE Main
Year: 2025
Date: 4 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Sets and Relations

JEE Main 2025 · 4 April · Evening Shift · Mathematics · Sets and Relations

Let A=\ -3,-2,-1,0,1,2,3\ and R be a relation on A defined by x R y...

Let

\mathrm{A}=\{-3,-2,-1,0,1,2,3\}

and R be a relation on

A

defined by

x R y

if and only if

2 x-y \in\{0,1\}

. 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 relations, respectively. Then

l+\mathrm{m} \mathrm{n}

is equal to :-

Options

A $18$
B $17$
C $15$
D $16$

Correct answer

B. $17$

Step-by-step solution

\begin{aligned} & \begin{array}{l}2 \mathrm{x}-\mathrm{y}=0 \\ \{0,0\}\{-1,-2\}\{1,2\} \\ 2 \mathrm{x}-\mathrm{y}=1\end{array} \\ & \{0,-1\}\{1,1\}\{2,3\}\{-1,-3\} \\ & \text{ Total }(0,0)(-1,-2),(1,2)(0,-1),(1,1)(2,3)(-1,-3) \\ & \text{ Reflexive } \quad \mathrm{m}=5 \quad & \ell=7 \\ & \text{ Symm. } \quad \mathrm{n}=5 \quad \ell+\mathrm{m}+\mathrm{n}=17 \\ & \text{ option (2) }\end{aligned}

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