Practicing Success

Target Exam

CUET

Subject

Mathematics

Chapter

Relations and Functions

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 relation is

Options:

reflexive and symmetric only

an equivalence relation

reflexive only

reflexive and transitive only

Correct Answer:

reflexive and transitive only

Explanation:

The correct answer is Option (4) → reflexive and transitive only

Clearly, corresponding to each $a ∈ A$ the ordered pair $(a, a) ∈ R$. So, R is reflexive on A.

R is not symmetric because $(6, 12) ∈ R$ but $(12, 6) ∉ R$.

R is a transitive relation on A.