A relation R is defined on set A = {1, 2, 3}, where R = {(1, 1), (2, 2

1.	A relation R is defined on set A = {1, 2, 3}, where R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}, then R is(A) reflexive but not transitive(B) reflexive but not symmetric(C) symmetric and transitive(D) neither symmetric nor reflexive
Answer» Answer is (B) Given : Set A = {1, 2, 3} and R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} (i) Reflexivity: (1, 1) ∈ R, (2, 2) ∈ R, (3, 3) ∈ R (a, a) ∈ R R is reflexive. (ii) Symmetricity: (1, 2) = (2, 1) ∉ R (1, 3) = (3, 1 ) ∉ R (2, 3) = (3, 2) ∉ R (a, b) ∈ R ⇒ (b, a) ∉ R So, R is not symmetric

A relation R is defined on set A = {1, 2, 3}, where R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}, then R is(A) reflexive but not transitive(B) reflexive but not symmetric(C) symmetric and transitive(D) neither symmetric nor reflexive

Answer»

Answer is (B)

Given : Set A = {1, 2, 3} and R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}

(i) Reflexivity: (1, 1) ∈ R, (2, 2) ∈ R, (3, 3) ∈ R

(a, a) ∈ R

R is reflexive.

(ii) Symmetricity: (1, 2) = (2, 1) ∉ R

(1, 3) = (3, 1 ) ∉ R

(2, 3) = (3, 2) ∉ R

(a, b) ∈ R ⇒ (b, a) ∉ R

So, R is not symmetric