The image contains a logic problem about translating specifications into English. The symbols used represent different printer and job states as follows:- $ F(p) $: Printer $ p $ is out of service.- $ B(p) $: Printer $ p $ is busy.- $ L(j) $: Print job $ j $ is lost.- $ Q(j) $: Print job $ j $ is queued.The problem asks to translate the following logical expressions into English:(a) $\exists p (F(p) \land B(p)) \rightarrow \exists j L(j)$- If there exists a printer $ p $ that is both out of service and busy, then there exists a print job $ j $ that is lost.(b) $\forall p B(p) \rightarrow \exists j Q(j)$- If every printer $ p $ is busy, then there exists a print job $ j $ that is queued.(c) $\exists j (\neg Q(j) \land L(j)) \rightarrow \exists p F(p)$- If there exists a print job $ j $ that is not queued and is lost, then there exists a printer $ p $ that is out of service.(d) $(\forall p B(p) \land \forall j Q(j)) \rightarrow \exists j \neg L(j)$- If every printer $ p $ is busy and every print job $ j $ is queued, then there exists a print job $ j $ that is not lost.

Answered: Image /qna-images/answer/63ce58c6-f988-4b62-8c58-02b1df475c6d.jpg

ranslate these specifications into English whe is busy,} L(j) is {Print job j is lost,} and Q a) p(F(p) ^ B(p)) → ‡jL(j) b) VpB(p) → jQ(j) (c) j(Q(j) ^ L(j)) → pF(p) d) (\pB(P)^\jQ(j)) → =jL(j)

ranslate these specifications into English whe is busy,} L(j) is {Print job j is lost,} and Q a) p(F(p) ^ B(p)) → ‡jL(j) b) VpB(p) → jQ(j) (c) j(Q(j) ^ L(j)) → pF(p) d) (\pB(P)^\jQ(j)) → =jL(j)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Concept explainers

Hash Table

A hash table also called a hash map, is a data structure that maps key-value pairs. The hash table can be used in complex systems to provide fast access and compact storage. A hash table is a structure that stores data in an abstract data type kind of associative array. It keeps data in an array format, with a distinct index value for every data value. If the index of the required data is known, then the data can be accessed very easily.

Question

The image contains a logic problem about translating specifications into English. The symbols used represent different printer and job states as follows:

- $ F(p) $: Printer $ p $ is out of service.
- $ B(p) $: Printer $ p $ is busy.
- $ L(j) $: Print job $ j $ is lost.
- $ Q(j) $: Print job $ j $ is queued.

The problem asks to translate the following logical expressions into English:

(a) $\exists p (F(p) \land B(p)) \rightarrow \exists j L(j)$

- If there exists a printer $ p $ that is both out of service and busy, then there exists a print job $ j $ that is lost.

(b) $\forall p B(p) \rightarrow \exists j Q(j)$

- If every printer $ p $ is busy, then there exists a print job $ j $ that is queued.

(c) $\exists j (\neg Q(j) \land L(j)) \rightarrow \exists p F(p)$

- If there exists a print job $ j $ that is not queued and is lost, then there exists a printer $ p $ that is out of service.

(d) $(\forall p B(p) \land \forall j Q(j)) \rightarrow \exists j \neg L(j)$

- If every printer $ p $ is busy and every print job $ j $ is queued, then there exists a print job $ j $ that is not lost.

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