Sets, Relations and FunctionsMCQPYQ Sep 24Question 1949 of 217
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Let A={1,2,3}\displaystyle A = \{1,2,3\} and consider the relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}\displaystyle R = \{(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)\} then R\displaystyle R is

Options

AReflexive but not symmetric
BReflexive but not transitive
CSymmetric and Transitive
DNeither symmetric nor transitive
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Correct Answer

✅ Option a — Reflexive but not symmetric

All Options:

  • AReflexive but not symmetric
  • BReflexive but not transitive
  • CSymmetric and Transitive
  • DNeither symmetric nor transitive

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Detailed Solution & Explanation

We are given set A={1,2,3}\displaystyle A = \{1,2,3\} and relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}\displaystyle R = \{(1,1), (2,2), (3,3), (1,2), (2,3), (1,3)\}.
Let's check the properties of R\displaystyle R:
1. **Reflexive**: For R\displaystyle R to be reflexive, it must contain (1,1),(2,2),(3,3)\displaystyle (1,1), (2,2), (3,3) since A={1,2,3}\displaystyle A = \{1, 2, 3\}.
Since these pairs are in R\displaystyle R, the relation is reflexive.
2. **Symmetric**: For R\displaystyle R to be symmetric, (a,b)∈R  ⟹  (b,a)∈R\displaystyle (a, b) \in R \implies (b, a) \in R.
Here, (1,2)∈R\displaystyle (1, 2) \in R but (2,1)∉R\displaystyle (2, 1) \notin R. Thus, the relation is not symmetric.
3. **Transitive**: For R\displaystyle R to be transitive, (a,b)∈R and (b,c)∈R  ⟹  (a,c)∈R\displaystyle (a, b) \in R \text{ and } (b, c) \in R \implies (a, c) \in R.
Here, (1,2)∈R\displaystyle (1, 2) \in R and (2,3)∈R  ⟹  (1,3)∈R\displaystyle (2, 3) \in R \implies (1, 3) \in R. Thus, the relation is transitive.
Therefore, the relation R\displaystyle R is reflexive but not symmetric.
Hence, **Option A** is the correct answer.

About This Chapter: Sets, Relations and Functions

Paper

Paper 3: Quantitative Aptitude

Weightage

3-5 Marks

Key Topics

Sets, Relations, Functions

This chapter covers Sets, Relations, Functions and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 3-5 Marks weightage. Focus on understanding core concepts rather than memorizing.

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