Correct Answer
✅ Option c — Perpendicular to is an equivalence relation
All Options:
- AParallel to is an equivalence relation
- BPerpendicular to is a symmetric relation
- CPerpendicular to is an equivalence relation
- DParallel to a reflexive relation
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Detailed Solution & Explanation
1. **"Parallel to" relation**:
- **Reflexive**: Every line is parallel to itself ().
- **Symmetric**: If , then .
- **Transitive**: If and , then .
Since it is reflexive, symmetric, and transitive, "Parallel to" is an equivalence relation. Hence, **Option A and Option D are TRUE**.
2. **"Perpendicular to" relation**:
- **Reflexive**: A line cannot be perpendicular to itself (). Thus, it is not reflexive.
- **Symmetric**: If , then . This is TRUE. Hence, **Option B is TRUE**.
- **Transitive**: If and , then and are parallel to each other (), not perpendicular. Thus, it is not transitive.
Since it is not reflexive or transitive, "Perpendicular to" is **NOT** an equivalence relation. Therefore, the statement "Perpendicular to is an equivalence relation" is **FALSE** (not TRUE).
*Note: The question asks which statement is NOT TRUE. Thus, Option C is the correct answer. The textbook answer key incorrectly lists Option B as correct.*
Hence, **Option C** 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 SyllabusExam Strategy Tip
This topic carries 3-5 Marks weightage. Focus on understanding core concepts rather than memorizing.
Key Concepts to Understand
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