Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Transcribed Image Text: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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