Mathematics · Sets and Relations

JEE Main 2026 — 6 April, Evening Shift — Question 40

Let $R = {(x,y) ∈ N×N : log_e(x+y) ≤ 2}.$ Then the minimum number of elements required to be added in $R$ to make it a transitive relation, is _____.

Answer: 15

Numerical answer — enter this value.

Step-by-step solution

$\mathrm{x}+\mathrm{y} \leq \mathrm{e}^{2}\left(\mathrm{e}^{2} \simeq 7.29\right)$ $\mathrm{R}=\{(1,1),(1,2),(1,4),(1,5),(1,6)\}$ $(2,1),(2,2),(2,3),(2,4),(2,5)$ $(3,1),(3,2),(3,3),(3,4)$ $(4,1),(4,2),(4,3)$ $(5,1),(5,2)$ $(6,1)$ For R to be transitive, we have to add $(6,2),(6,3),(6,4),(6,5),(6,6)$ $(5,3),(5,4),(5,5),(5,6)$ $(4,4),(4,5),(4,6)$ $(3,5),(3,6)$ $(2,3)$ $=15$ elements

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Exam: JEE Main 2026
Paper: 6 April, Evening Shift
Subject: Mathematics
Chapter: Sets and Relations
Topic: Number of Relations