In: Advanced Math
Determine if the binary relation <= is a partial order on A in the following cases:
(a) A = N × N and (a1, b1) (a2, b2) ⇔ a1 <= a2 for (a1, b1),(a2, b2) ∈ A
(b) X = {1, 2, 3, 4}, A = P(X) and a <= b ⇔ #a <= #b for a, b ∈ A (Here #a denotes the number of elements in the set a)
(c) A = N and a <= b ⇔ ∃k ∈ N : a^k = b