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Ideal occurrence of an event (projector)  leads to the known change of a state (density operator)  into  (the Lüders state). It is shown that two events  and  give the same Lüders  state if and only if the equivalence relation   is valid. This relation determines equivalence classes. The set of them and each class, are studied in detail. It is proved that the range projector  of the Lüders state can be evaluated as  , where  denotes the greatest lower bound, and  is the null projector of  .  State-dependent implication  extends absolute implication (which, in turn, determines the entire structure of quantum logic).  and  are investigated in a closely related way to mutual benefit. Inherent in the preorder  is the state-dependent equivalence , defining equivalence classes in a given Boolean subalgebra. The quotient set, in which the classes are the  elements,  has itself a partially ordered structure, and so has each class. In a  complete Boolean subalgebra, both structures are complete lattices. Physical meanings are  discussed

State-Dependent Implication and Equivalence in Quantum Logic