Computer Science - Discrete Math Review

Please answer 2 a&b . Explain thoroughly, so I can understand. Thanks

2a) Evaluate the proposition x.y.P(x,y) y.x.P(x,y) for an unknown predicate P. Could the statement be true? Must the statement be true for all P?

Give a specific P (with domains for x and y) where it is either true or false. Prove that it is true for all P , or show a contradiction.

2b) Assume a directed acyclic graph is encoded as a relation R. Give a concise proposition stating that R is irreflexive (i.e., that no nodes have edges to themselves).