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: 41

Answer

a) P(x) :if there is a disk with more than 10 kilobytes of free space Q(x): At least one mail message, among the nonempty set of messages, can be saved so, P(x) ->Q(x) b) It work like this , " A whenever B" can be written as " A if B" P(x): Whenever (if) there is an active alert Q(x): all queued messages are transmitted. P(x) -> Q(x) c) According to the authoritative logician S.C.Kleene, Mathematical logic, Dover (1967), page 63: "A except when B" must be usually symbolized with A∨B and sometimes with "A or B but not both", i.e. (A∨B)∧¬(A∧B). Thus, with: "The diagnostic monitor tracks the status of all systems except the main console", (i) $∀s[\text {TracStat}(\text{DiaMon},s) \lor \text {MainCons}(s)]$, that is equivalent to: $∀s[¬ \text {MainCons}(s) \to \text {TracStat}(\text{DiaMon},s)]$. (ii) $∀s[(\text {TracStat}(\text{DiaMon},s) \lor \text {MainCons}(s)) \land \lnot (\text {TracStat}(\text{DiaMon},s) \land \text {MainCons}(s))].$ d) P(x):the host of the call did not put on a special list was billed. :Q(x)Each participant on the conference call P(x) -> Q(x)

Work Step by Step

a) We can use the analogy of the a if b b) Whenever (if) ........, then .... c) explanation given in the answer d) whom (if) ........, then ....
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.