Question

Let R be the relation in the set {1,2,3,4} given by R= {(1,2), (2,2), (1,1), (4,4), (1,3), (3,3), (3,2)}. Choose the correct answer.

• A. R is reflexive and symmetric but not transitive.
• B. R is reflexive and transitive but not symmetric.
• C. R is symmetric and transitive but not reflexive.
• D. R is an equivalence relation.

Answer 1

Answer: (B)

R is reflexive and transitive but not symmetric.

Answer 2

R =${(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}$
It is seen that $(a, a) ∈ R$, for every $a ∈{1, 2, 3, 4}$.
∴ R is reflexive. It is seen that $(1, 2) ∈$R, but $(2, 1) ∉ R.$
∴R is not symmetric. Also, it is observed that $(a, b), (b, c) ∈ R ⇒ (a, c) ∈ R$ for all $a, b, c ∈ {1, 2, 3, 4}$.
∴ R is transitive. Hence, R is reflexive and transitive but not symmetric.

The correct answer is B.