Q1670: A relation R on set $A=\{1,2,3\}$ defined as $R=\{(1,1), (2,...

Class CBSE Class 12 Mathematics Relations and Functions Q #1670

COMPETENCY BASED

APPLY

1 Marks 2026 AISSCE(Board Exam) MCQ SINGLE

A relation R on set $A=\{1,2,3\}$ defined as $R=\{(1,1), (2,2), (1,2)\}$ is

(A) Reflexive only

(B) Reflexive and Transitive

(D) Transitive only

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Correct Answer: D

AI Tutor Explanation

Detailed Solution

Step 1: Check for Reflexivity

A relation $R$ on set $A$ is reflexive if $(a, a) \in R$ for all $a \in A$. Here, $A = \{1, 2, 3\}$. For $R$ to be reflexive, it must contain $(1, 1), (2, 2),$ and $(3, 3)$. Since $(3, 3) \notin R$, the relation is not reflexive.

Step 2: Check for Symmetry

A relation $R$ is symmetric if $(a, b) \in R \implies (b, a) \in R$. Here, $(1, 2) \in R$, but $(2, 1) \notin R$. Therefore, the relation is not symmetric.

Step 3: Check for Transitivity

A relation $R$ is transitive if $(a, b) \in R$ and $(b, c) \in R \implies (a, c) \in R$. Checking the pairs: - $(1, 1)$ and $(1, 2) \implies (1, 2) \in R$ (True) - $(1, 2)$ and $(2, 2) \implies (1, 2) \in R$ (True) - $(2, 2)$ and $(2, 2) \implies (2, 2) \in R$ (True) Since all conditions hold, the relation is transitive.

Final Answer: Transitive only

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Pedagogical Audit

Bloom's Analysis: This is an APPLY question because the student must apply the formal definitions of reflexive, symmetric, and transitive relations to a specific set of ordered pairs.

Knowledge Dimension: CONCEPTUAL

Justification: The question tests the understanding of abstract mathematical properties (relations) rather than rote memorization of facts.

Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. It aligns with the NCERT Chapter 1 (Relations and Functions) learning outcomes regarding the classification of relations.

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