Relations R1 and R2 on the set {1, 2, 3, 4, 5} defined by the rule (x, y) ∈ R1 if x + y ≤ 6 and (x, y) ∈ R1 if x = y − 1. (For each part, if the answer is yes, explain, otherwise, provide a counter example. You can use digraphs for the explanation).

•Check whether or not R1 is reflexive, symmetric, antisymmetric, and transitive.

•What is the inverse of R1?

•Provide the digraph.

•Check whether or not R2 is reflexive, symmetric, antisymmetric, and transitive.

•What is the inverse of R2?

•Provide the digraph.