Let X be a set. Let P be a set of subsets of X such that: OEP; the union of all sets AEP is X. Note that these are clauses (a) and (c) of the definition of a partition (Definition 1.5). Now define a relation R on the set X by R-1(x,y): xEA and ye A for some AE P1, as in Theorem 1.7(b). Which of the following is true? Select one: O a. R must be symmetric and transitive but might not be reflexive. Ob. R must be an equivalence relation, but [[xle: xEX) might not be equal to P. Oc R must be reflexive and transitive but might not be symmetric. Od. R must be an equivalence relation, and [[xle :x EX] must equal P Oe R must be reflexive and symmetric but might not be transitive.