Get solution: Assign a grade of A (correct), C (partially correct), or F (failure) to
Chapter 3, Problem 15(choose chapter or problem)
Assign a grade of A (correct), C (partially correct), or F (failure) to each. Justifyassignments of grades other than A. (a) Claim.Proof.(b) Claim. If and then .Proof. Suppose Then there existswith . But implies that andwhereas implies that and However,and so and This is a contradiction. Therefore,(c) Claim. If and thenProof. Suppose ThenTherefore (d) Claim. If and thenProof. To show suppose Choose anyThen But since ThusThis proves A proof of is similar. Therefore,(e) Claim. Let R and S be relations from A to B and from B to C, respectively.ThenProof. The pairTherefore,(f) Claim. Let R be a relation from A to B. ThenProof. Suppose Choose any such thatThen, Thus Therefore,(g) Claim. Suppose R is a relation from A to B. ThenProof. Let Then for some andThus Since and Thus(x, y) = (x, x) and so x A, (x, y) IA.(z, y)
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