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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!

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

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