(8 pt.) Consider the following three hash functions h1, h2, h3 that each hash a universe U of keys to one of n = 3 buckets.

h1(key) = length of the key mod 3

h2(key) = numeric value of the rst digit of key mod 3

h3(key) = sum of the digits of the key mod 3

(a) For which universes U is the hash family H = {h1,h2} universal? Circle all that apply.

(A) U = {111,222,333} (B) U = {1,22,333} (C) U = {1,11,111} (D) U = {1,2,3} (E) U = {1,23,333}

(b) For which universes U is the hash family H = {h1,h2,h3} universal? Circle all that apply.

(A) U = {111,222,333} (B) U = {1,22,333} (C) U = {1,11,111} (D) U = {1,2,3} (E) U = {1,23,333}

The answer is (a): (B),(E), (b): (B),(C),(D),(E)

Why the answer is above??

I don't solve this problem.

Actually I don't know how to calculate the probability of required set(U)....

How to calculate the probability of each set(U) in question?