Find the smallest relation containing the relation
$$R=\{ (1,2),(2,1),(2,3),(3,4),(4,1) \}$$ that is
Reflexive and transitive
Reflexive, transitive and symmetric
Well this seems easy to do. However, I'm not sure whether the question is meant to find the (for the first part) the reflexive and transitive closures, or is it something else?
If it's a closure case, then the first part would be: $$R=\{ (1,2),(2,1),(2,3),(3,4),(4,1),(1,1),(2,2),(3,3),(4,4),(1,3),(2,4),(3,1),(4,2)\}$$
But this doesn't seem right for some reason and just wanted to clarify what the question is asking.