Discrete Maths Relations on the set {1,2,3,4}

Question

I just want to make sure that I am doing these correctly. Here is what I have:

1. Reflexive, symmetric, antisymmetric and transitive: And i have - {(1,1) (2,2) (3,3) (4,4)}.

2. not Reflexive, not symmetric and not transitive: And i have - {(1,1) (2,2) (3,3)}.

3. not Reflexive, symmetric and transitive: And i have - {(1,2) (2,3) (3,4) (1,4)}.

4. Reflexive, symmetric and transitive: And i have - {(1,1) (2,2) (3,3) (4,4)}.

Help is very much appreciated. Thank you (discrete mathematics)

Answer 1

• Your first and fourth relation work. The first relation is forced to be the identity, but the fourth relation doesn't have to be (for example, you could add the ordered pairs $(1, 2), (2, 1)$ without violating any properties).

• Your second and third relations need to be switched.