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

(b) R is reflexive and transitive but not symmetric.

Explanation::

Let R be the relation with set {1,2, 3,4}, given by R = {(1,2), (2,2), (1,1), (4,4), (1,3), (3,3), (3,2)}.

(a) (1, 1), (2, 2), (3, 3), (4, 4) ∈ R ⇒ R is reflexive.

(b) (1, 2) ∈ R but (2, 1) does not belongs to R.

∴ R is not symmetric.

(c) If (1, 3) ∈ R and (3, 2) ∈ R, then (1, 2) also ∈ R.

∴ R is transitive.