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MIT6_042JS10_lec04_prob

MIT6_042JS10_lec04_prob - Massachusetts Institute of...

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Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science February 10 Prof. Albert R. Meyer revised February 3, 2010, 2 minutes In-Class Problems Week 2, Wed. Problem 1. Prove by truth table that OR distributes over AND : [ P OR ( Q AND R )] is equivalent to [( P OR Q ) AND ( P OR R )] (1) Problem 2. This problem 1 examines whether the following specifications are satisfiable : 1. If the file system is not locked, then (a) new messages will be queued. (b) new messages will be sent to the messages buffer. (c) the system is functioning normally, and conversely, if the system is functioning nor- mally, then the file system is not locked. 2. If new messages are not queued, then they will be sent to the messages buffer. 3. New messages will not be sent to the message buffer. (a) Begin by translating the five specifications into propositional formulas using four proposi- tional variables: L ::= file system locked , Q ::= new messages are queued , B ::= new messages are sent to the message buffer , N ::= system functioning normally . (b) Demonstrate that this set of specifications is satisfiable by describing a single truth assignment for the variables L, Q, B, N and verifying that under this assignment, all the specifications are true.
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