# Relationship: reflexive, symmetric, antisymmetric, transitive

## Homework Statement

Determine which binary relations are true, reflexive, symmetric, antisymmetric, and/or transitive.

The relation R on P = {a, b, c} where R = {(a, a), (a, b), (a, c), (b, c), (c, b)}

## The Attempt at a Solution

Not reflexive because there is no (b, b) or (c, c).
Not symmetric because there is (a, b), but not (b, a).
Not antisymmetric because there is (b, c) and (c, b).
Not transitive because there is (b, c) and (c, b) but no (b, b).

Is it possible for there to not be any binary relations?

Dick
Homework Helper

## Homework Statement

Determine which binary relations are true, reflexive, symmetric, antisymmetric, and/or transitive.

The relation R on P = {a, b, c} where R = {(a, a), (a, b), (a, c), (b, c), (c, b)}

## The Attempt at a Solution

Not reflexive because there is no (b, b) or (c, c).
Not symmetric because there is (a, b), but not (b, a).
Not antisymmetric because there is (b, c) and (c, b).
Not transitive because there is (b, c) and (c, b) but no (b, b).

Is it possible for there to not be any binary relations?

It is a binary relation, but as you say, it doesn't have any of those properties.

Yeah, that's what I thought. Thanks for the help again.