Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 1 - Section 1.4 - Predicates and Quantifiers - Exercises - Page 55: 39

Answer

a) If there is a printer that is out of service and is busy, then there is a print, job that is lost. b) If all printers are busy, then there is a print job that is queued. c) If there exists a print job that is lost and queued, then there exists a printer that is out of service. d) If all printers are busy and all print jobs are queued, then there exists a print job that is lost.

Work Step by Step

a) $\rightarrow$ means IF-THEN, $\land$ means AND, $\exists$ means THERE EXISTS. If there is a printer that is out of service and is busy, then there is a print, job that is lost. b)$\rightarrow$ means IF-THEN, $\forall$ means ALL, $\exists$ means THERE EXISTS. If all printers are busy, then there is a print job that is queued. c) $\rightarrow$ means IF-THEN, $\forall$ means ALL, $\exists$ means THERE EXISTS. If there exists a print job that is lost and queued, then there exists a printer that is out of service. d) $\rightarrow$ means IF-THEN, $\forall$ means ALL, $\exists$ means THERE EXISTS and $\forall$ means ALL. If all printers are busy and all print jobs are queued, then there exists a print job that is lost.
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