Let R be a relation on N × N defined by (a, b) ~R~(c, d) if and only if a d(b-c)=b c(a-d). Then R is

(D) symmetric but neither reflexive nor transitive

(A) symmetric and transitive but not reflexive

(B) reflexive and symmetric but not transitive

(C) transitive but neither reflexive nor symmetric

Sets, Relations and Functions: JEE Main 2023 Mathematics question

JEE Main 2023 · 31 Jan, Morning shift · Q5387

JEE Main 202331 Jan, Morning shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let

\mathrm{R}

be a relation on

\mathrm{N} \times \mathbb{N}

defined by

(a, b) ~\mathrm{R}~(c, d)

if and only if

a d(b-c)=b c(a-d)

. Then

\mathrm{R}