Let X be a set. Let P be a set of subsets of X such that: • ØEP; • if A and B are distinct elements of P, then ANB=0. Note that these are clauses (a) and (b) of the definition of a partition (Definition 1.5). Now define a relation R on the set X by R={(x, y): xe A and ye A for some A € P), as in Theorem 1.7(b). Which of the following is tru Select one: O a. R must be an equivalence relation, and {[x]: xex) must equal P. O b. R must be an equivalence relation, but { [x]: xe X} might not be equal to P. 0 с. R must be reflexive and transitive but might not be symmetric. O d. R must be reflexive and symmetric but might not be transitive. O e. R must be symmetric and transitive but might not be reflexive.

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