Solved: Let R be a quasi-ordering and let S be the

Chapter 8, Problem 8.38

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Let R be a quasi-ordering and let S be the relation on the set of equivalence classes of R n R - I 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 (v) operations by x !\ Y = glb(x, y) and x v y = lub(x , y).

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