How can I prove reflexive closure preserves symmetry, anti-symmetry, and transitivity?

Question

Let R be a relation in A. Let R' be the reflexive closure of R. IE in the graph of R, each possible self loop is completed, yielding R'. How can I prove that this operation on the graph will preserve all three properties above in all cases? Is there a way of doing this in a graph? Would a prose explanation suffice, as in by definitions? Furthermore how would I do the same for a symmetric closure on a reflexive relation?