Suppose H is a collection of hash functions, where each hash function h, is mapping the universe U of keys to {0, 1, · · · , m − 1}. Also, suppose that for every fixed pair (x, y) of keys (where x 6= y), and for any uniformly selected hash function h, the pair (h(x), h(y)) is equally likely to be any of the m2 pairs of elements from {0, 1, · · · , m − 1} (The probability is taken only over the random choice of the hash function.) Prove that H is a universal hashing.