- #1

mathmari

Gold Member

MHB

- 5,049

- 7

I am looking at the following:

There are the terms reflexive, symmetric, antisymmetric and transitive.

Give for each combination of the properties (if possible) a set $M$ and a relation $R$ on $M$, such that $R$ satisfies these properties. What is meant exactly? Every possible combination? So do we have to give a set and a relation that satisfies the below properties?

- reflexive, symmetric
- reflexive, antisymmetric
- reflexive, transitive
- symmetric, antisymmetric
- symmetric, transitive
- antisymmetric, transitive
- reflexive, symmetric, antisymmetric
- reflexive, symmetric, transitive
- reflexive, antisymmetric, transitive
- symmetric, antisymmetric, transitive
- reflexive, symmetric, antisymmetric transitive

(Wondering)