Let R be a quasi-ordering and let S be the relation on the

Chapter 12, Problem 38E

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Let R be a quasi-ordering and let S be the relation on the set of equivalence classes of R ? R–1 such that (C, D) belongs to S, where C and D are equivalence classes of R, if and only if there are elements c of C and d of D such that (c, d) belongs to R. Show that S is a partial ordering.Let L be a lattice. Define the meet (?) and join (?) operations by x ? y = glb(x, y) and x ? y = lub(x, y).

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