Let A = {0, 1, 2, 3} and define a relation R on A as follows:R = {(0,

1.	Let A = {0, 1, 2, 3} and define a relation R on A as follows:R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}.Is R reflexive? symmetric? transitive?
Answer» R is reflexive and symmetric, but not transitive since for (1, 0) ∈ R and (0, 3) ∈ R whereas (1, 3) ∉ R. Since A = {0, 1, 2, 3} R : A → A Since, 0, 1, 2, 3 \(\in\) A and (0, 0), (1, 1), (2, 2) (3, 3) \(\in\) R Hence, for each a \(\in\) A (a, a) \(\in\) R ∴ R is a reflexive relation. Since, (0, 1) ∈ R Then (1, 0) ∈ R (0, 3) ∈ R Then (3, 0) ∈ R Hence, if (a, b) ∈ R Then (b, a) ∈ R ∴ Relation R is symmetric relation. Since, (1, 0) ∈ R, (0, 3) ∈ R but (1, 3) \(\notin\) R ∴ Relation R is not transitive.

Let A = {0, 1, 2, 3} and define a relation R on A as follows:R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}.Is R reflexive? symmetric? transitive?

Answer»

R is reflexive and symmetric, but not transitive since for (1, 0) ∈ R and (0, 3) ∈ R whereas (1, 3) ∉ R.

Since A = {0, 1, 2, 3}

R : A → A

Since, 0, 1, 2, 3 \(\in\) A

and (0, 0), (1, 1), (2, 2) (3, 3) \(\in\) R

Hence, for each a \(\in\) A

(a, a) \(\in\) R

∴ R is a reflexive relation.

Since, (0, 1) ∈ R Then (1, 0) ∈ R

(0, 3) ∈ R Then (3, 0) ∈ R

Hence, if (a, b) ∈ R Then (b, a) ∈ R

∴ Relation R is symmetric relation.

Since, (1, 0) ∈ R, (0, 3) ∈ R but (1, 3) \(\notin\) R

∴ Relation R is not transitive.