Now solved: Assign a grade of A (correct), C (partially correct), or F (failure) to
Chapter 3, Problem 20(choose chapter or problem)
Assign a grade of A (correct), C (partially correct), or F (failure) to each.Justify assignments of grades other than A.(a) Claim. Let A be a set with a partial order R. If and sup(C)and sup(B) exist, then sup(C) sup(B).Proof. sup(B) is an upper bound for B. Therefore, sup(B) is an upperbound for C. Thus sup(C) sup(B). (b) Claim. Let A be a set with a partial order R. If u is an upperbound for B, and then sup(B) exists andProof. Since Since u is an upper bound,Thus(c) Claim. For A, with the usual ordering,Proof. If then or Therefore orThus for all x in ThereforeAlso and so bypart (a), and Thereforesup(A)+sup(B) sup(AB). Thus sup(A)+sup(B) = sup(AB).sup(
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