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

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)}

it is seen that (a,a)∈ R for every a∈{1,2,3,4}

so,R is feflexive.

it is seen that (a,b) = (b,a) ∈ R

because, (1,2)∈ R but (2,1) ∉R

so, R is not symmetric.

it is seen that (a, b), (b, c) ∈ R ⇒ (a, c) ∈ R for all a, b, c ∈ {1, 2, 3, 4}.

so, R is transitive.

hence, R is reflexive and transitive but not symmetric.

so, option (B) is correct.