Disjoint Sets are a data structure for keeping track of associations among items in a larger system. a) In Disjoint Sets, we have the option of using two techniques: union by rank and path compression. What are the benefits of union by rank? What are the benefits of path compression? b) Assume you have a Disjoint Set instance which is logically represented as the following set of trees. Show how this set could be represented in the following sets array (table below), assuming union by rank.

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Predicates

A predicate is a function defined with set of variables, which returns the result True or False. The output of a predicate is a Boolean value as a response when given a set of parameters: