Choose the correct option. The relation R = {(1, 1), (2, 2), (3, 3),

1.	Choose the correct option. The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on a set A = {1, 2, 3} is(a) reflexive, transitive but not symmetric (b) reflexive, symmetric but not transitive (c) symmetric, transitive but not reflexive (d) reflexive but neither symmetric nor transitive.
Answer» R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3}. (i) Since (1, 1), (2, 2), (3, 3) ∈ R ⇒ R is reflexive. (ii) (1, 2) ∈ R but (2, 1) ∉ R ⇒ R is not symmetric. (iii) (1, 2) ∈ R, (2, 3) ∈ R and (1, 3) ∈R ⇒ R is transitive. ∴ Option (a) is the right answer.

Choose the correct option. The relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on a set A = {1, 2, 3} is(a) reflexive, transitive but not symmetric (b) reflexive, symmetric but not transitive (c) symmetric, transitive but not reflexive (d) reflexive but neither symmetric nor transitive.

Answer»

R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)} on set A = {1, 2, 3}.

(i) Since (1, 1), (2, 2), (3, 3) ∈ R ⇒ R is reflexive.

(ii) (1, 2) ∈ R but (2, 1) ∉ R ⇒ R is not symmetric.

(iii) (1, 2) ∈ R, (2, 3) ∈ R and (1, 3) ∈R ⇒ R is transitive.

∴ Option (a) is the right answer.

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