answer c 17. Evaluation of ProofsSee the instructions for Exercise (19) on page 100 from Section 3.1.(a) Let A, B, and C be subsets of some universal set. If A ¢ B andB¢ C, then A 4 C.Proof. We assume that A, B, and C are subsets of some universal setand that A Z B and B ¢ C. This means that there exists an element xin A that is not in B and there exists an element x that is in B and not inC. Therefore, x e A and x ¢ C, and we have proved that A ¢ C. I(b) Let A, B, and C be subsets of some universal set. If AO B = AN C,then B = C.Proof. We assume that A N B = A n C and will prove that B = C.We will first prove that B C C.So let x e B. If x € A, then x e A O B, and hence, x e ANC.From this we can conclude that x e C. If x ¢ A, then x ¢ AN B,and hence, x ¢ ANC. However, since x ¢ A, we may conclude thatхеС. Therefore, в С.The proof that C C B may be done in a similar manner. Hence, B =С.(c) Let A, B, and C be subsets of some universal set. If A ¢ B andBC C, then A g C.Proof. Assume that A 4 B and BC C. Since A ¢ B, there existsan element x such that x e A and x ¢ B. Šince B C Ĉ, we mayconclude that x ¢ C. Hence, x e A and x ¢ C, and we have provedthat A 4 C.

Name: answer c 17. Evaluation of ProofsSee the instructions for Exercise (19
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Description: answer c 17. Evaluation of ProofsSee the instructions for Exercise (19) on page 100 from Section 3.1.(a) Let A, B, and C be subsets of some universal set. If A ¢ B andB¢ C, then A 4 C.Proof. We assume that A, B, and C are subsets of some universal se