Topic: Discrete Mathematics and its Applications" Chapter 9:Equivalence Relations and Partial Orderings.

9. hash function H : {0,1)" {0,1)" maps a bit string of length n to a bit string of length k. Hash functions are used to give a short label to a long string. The set of all "collisions" with a given string s defines an equivalence class for a given hash function H, that is: (a) What is the average cardinality of the equivalence classes [s]H in terms of n and k, where n > k? (b) What is the probability for any two random bit strings from s,te { 0, 1 }n that