Q. Let $R =${(3, 3), (6, 6), (9, 9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set $A = \{ 3,\ 6,\ 9,\ 12\}$. The relation is
A) Reflexive and symmetric only
B) An equivalence relation
C) Reflexive only
D) Reflexive and transitive only
Explanation
(d)
Since, $(3,\ 3),\ (6,\ 6),\ (9,\ 9),\ (12,\ 12) \in R \Rightarrow R$ is reflexive.
Now, $(6,\ 12) \in R$ but $(12,\ 6) \notin R \Rightarrow R$ is not symmetric.
Also, $(3,\ 6),\ (6,\ 12) \in R \Rightarrow (3,\ 12) \in R$
$\Rightarrow R$ is transitive.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.