Let a relation R on $\mathbb{N}\times\mathbb{N}$ be defined as: $(x_1,y_1)\ \mathrm{R}\ (x_2,y_2)$ if and only if $x_1\le x_2$ or $y_1\le y_2$. Consider the two statements: (I) R is reflexive but not symmetric. (II) R is transitive Then which one of the following is true?

Neither (I) nor (II) is correct.

JEE Main 2024 · MathsMultiple choiceTwo statementsMediumConceptual

JEE Main 4 April 2024, Shift 2, Maths Q1

Question 1 of 90 in this shift, Maths question 1 of 30, Section A.

Let a relation R on

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

be defined as:

(x_1,y_1)\ \mathrm{R}\ (x_2,y_2)

if and only if

x_1\le x_2

y_1\le y_2

. Consider the two statements: (I) R is reflexive but not symmetric. (II) R is transitive Then which one of the following is true?

(1)Only (I) is correct.Official answer
(2)Only (II) is correct.
(3)Both (I) and (II) are correct.
(4)Neither (I) nor (II) is correct.

Official answer

Option 1

NTA final key.

Chapter: Relations and Functions
Topic: Sets and Relations
Idea tested: Relation Types

Same idea in other shifts

Asked 12× in all

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8 Apr 2024, Shift 2 · Q1Let $A = \{2, 3, 6, 8, 9, 11\}$ and $B = \{1, 4, 5, 10, 15\}$ . Let R be a relation on $A \times B$ defined by $(a, b)R(c, d)$ if and only…HardSingle correct
27 Jan 2024, Shift 1 · Q1Let $S=\{1,2,3,\ldots,10\}$ . Suppose M is the set of all the subsets of S, then the relation $R=\{(A,B): A\cap B\neq\phi;\ A,B\in M\}$ is :EasySingle correct
29 Jan 2024, Shift 1 · Q2Let R be a relation on $\mathbb{Z}\times\mathbb{Z}$ defined by $(a, b)\,R\,(c, d)$ if and only if $ad-bc$ is divisible by 5. Then R isMediumSingle correct
31 Jan 2024, Shift 2 · Q21Let $A=\{1,2,3,\ldots,100\}$ . Let $R$ be a relation on $A$ defined by $(x,y)\in R$ if and only if $2x=3y$ . Let $R_1$ be a symmetric…MediumNumerical value
8 Apr 2023, Shift 2 · Q1Let $A = \{1, 2, 3, 4, 5, 6, 7\}$ . Then the relation $R = \{(x, y) \in A \times A : x + y = 7\}$ isEasySingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 108 of the 174 JEE Main shifts held from 2017 to 2026.