Problem 1 We can view C as a binary relation between sets, because given any two sets A, B, either A C B or A & B. Let S be an arbitrary nonempty set and P(S) its power set. Is C a partial order on P(S)? Is it also a total order? Explain. Problem 2. Suppose R is a total order on S where |S) is finite. Prove that there exists a mapping f : S - R such that f(x) > f(y) if and only if x Ry. Problem 3. Is d(x, y) = (x2 - y2| a metric on R2? Explain