Relations & Functions
Types of Relations
Grade 12
Question:
<p>Let \(R = \{(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9)\}\) be a relation on the set \(A = \{3, 6, 9, 12\}\). The relation is</p>
<p>(a) an equivalence relation</p>
<p>(b) reflexive and symmetric only</p>
<p>(c) reflexive and transitive only</p>
<p>(d) reflexive only</p>
Step-by-Step Solution
Key Concept: Test each property of relations: reflexivity, symmetry, and transitivity independently
<p><strong>Analysis:</strong> Check reflexivity: All elements are related to themselves ✓. Check symmetry: (6,12) ∈ R but (12,6) ∉ R, so not symmetric ✗. Check transitivity: (3,9) and (9,9) implies (3,9) ∈ R ✓; (6,12) and (12,12) implies (6,12) ∈ R ✓. The relation is reflexive and transitive only.</p><p>∴ Answer is (c).</p>
Correct Answer: c