# Identifying Properties of Relations

I know this will seem like a very basic question but I want to verify that I am clear on these concepts. So for the following relations, I have to determine whether they are reflexive, non reflexive, irreflexive, symmetric, asymmetric, antisymmetric and transitive. Here's what I have so far:

1. { < x, y > ∈ D × D : x and y have the same age } : reflexive, symmetric, transitive

2. { < x, y > ∈ D × D : x is at least as old as y } : reflexive, transitive (this relation isn't asymmetric because if x is at least as old as y, x may be older so y wouldn't be at least as old as x. However, I'm thinking that it may be antisymmetric: if x is at least as old as y and y is at least as old as x, then x and y are the same age?)

3. { < x, y > ∈ D × D : x is exactly one year older than y } : non reflexive, irreflexive, asymmetric

4. { < x, y > ∈ D × D : x is twice as old as y } : non reflexive, irreflexive, asymmetric

5. { < x, y > ∈ D × D : x is French and y is not or viceversa } : non reflexive, irreflexive, symmetric

Thanks so much for the help!

• 3,4 not transitive – William Elliot Oct 13 '18 at 3:46