Let A = {1, 2, 3, 4, 5, 6} and let R be the relation on the power set of A defined by X R Y iff X is a subset of Y .

(a) Prove that R is reflexive, antisymmetric, and transitive.

(b) How many ordered pairs are in R? (Hint: For a subset X of size m, how many subsets

Y satisfy XRY ?)