hw1_solutions

# hw1_solutions - COMP 201 Fall 2010 HW1 SOLUTIONS 1.1/42 No...

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COMP 201, Fall 2010 HW1 SOLUTIONS 1.1/42 No, because it cannot have a truth value. Indeed, this statement causes a paradox. Let's assume that it is true. Then, it is asserting that it is false, which is a contradiction. Let's assume that it is false. Then, since the statement says that it is false and it is in reality false, then it must be true, which is, again, a contradiction. Therefore, this assertion cannot be a proposition. 1.1/52 A set of propositional expressions is consistent if there is an assignment of truth values to the variables in the expressions that makes each expression true. In other words; to prove the consistency of the specifications, we should seek a truth value assignment combination for the variables that makes all the expressions true. L : The file system is locked. Q : New messages will be queued. N : The system is functioning normally. B : New messages will be sent to the message buffer. Specifications: If the file system is not locked, then new messages will be queued: ¬ L Q If the file system is not locked, then the system is functioning normally and conversely: ¬ L N If the new messages are not queued, then they will be sent to the message buffer: ¬ Q B If the file system is not locked, then the new messages will be sent to the message buffer: ¬ L B New messages will not be sent to the message buffer: ¬ B The following truth value assignment makes all these expressions true: B: False, N: False, Q: True, L : True Thus the table below shows the consistency of the system: ¬ L Q F T T ¬ L N F F T ¬ Q B F F T ¬ L B F F T ¬ B T T Please be aware that there may be other truth value assignments that make all expressions true, but one is sufficient to show the consistency.

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