CBSE Class 12 Mathematics Relations and Functions Q #2130
COMPETENCY BASED
APPLY
3 Marks Generic-Curriculum SA
Let $A = \text{a set of people}$. Let $a R b$ if and only if $a$ and $b$ are brothers. (i) Is the relation reflexive? (ii) Is the relation symmetric? (iii) Is the relation an equivalence relation?
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Detailed Solution

Step 1: Analyze Reflexivity

A relation $R$ is reflexive if $a R a$ for all $a \in A$. Here, $a R a$ means a is a brother of a. Since a person cannot be their own brother, the relation is not reflexive.

Step 2: Analyze Symmetry

A relation $R$ is symmetric if $a R b \implies b R a$. If a is a brother of b, then b must also be a brother of a. Thus, the relation is symmetric.

Step 3: Analyze Equivalence Relation

An equivalence relation must be reflexive, symmetric, and transitive. Since the relation fails the reflexivity test, it cannot be an equivalence relation.

Final Answer: (i) No, (ii) Yes, (iii) No

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student must apply the formal definitions of mathematical relations to a real-world scenario involving kinship.
Knowledge Dimension: CONCEPTUAL
Justification: The question tests the understanding of the underlying properties (reflexivity, symmetry, transitivity) rather than rote memorization of formulas.
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, requiring students to evaluate logical properties of relations.

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