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)}.

Options

• R is reflexive and symmetric but not transitive.

• R is reflexive and transitive but not symmetric.

• R is symmetric and transitive but not reflexive.

• R is equivalence relation.

Answer 1

R is reflexive and transitive but not symmetric.

Explanation:

Here, R = {(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3,2)}

Since (a, a) ∈ R, for every a ∈ {1, 2, 3, 4}.

Therefore, R is reflexive.

Now, since (1, 2) ∈ R but (2, 1) ∈ R but. Therefore, 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}

Therefore, R is transitive. Hence, R is reflexive and transitive but not symmetric.