Question

Let \( R = \{(3,3), (6,6), (9,9), (12,12), (6,12), (3,9), (3,12), (3,6)\} \) be a relation on the set \( A = \{3,6,9,12\} \). Then, the relation is:

• A. an equivalence relation
• B. reflexive and symmetric
• C. reflexive and transitive
• D. only reflexive

Hint:

Equivalence relations must be reflexive, symmetric, and transitive.

Answer 1

The Correct Option is C

Step 1: All elements \((a,a)\) are present, so the relation is reflexive.
Step 2: If \((a,b)\) and \((b,c)\) are in \(R\), then \((a,c)\) is also in \(R\), hence transitive.
Step 3: Relation is not symmetric as \((6,3)\) is not present.