Problem: System Specifications Consistency

Problem:

Determine whether these system specifications are consistent:
­"The diagnostic message is stored in the buffer or it is retransmitted."
"The diagnostic message is not stored in the buffer."
"If the diagnostic message is stored in the buffer, then it is retransmitted."

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Solution:

To determine whether these specifications are consistent, we first express them using logical expressions. Let p denote "The diagnostic message is stored in the buffer" and let q denote "The diagnostic message is retransmitted." The specifications can then be written as p v q, -,p, and p -* q. An assignment of truth values that makes all three specifications true must have p false to make -'p true. Because we want p v q to be true but p must be false, q must be true. Because p -* q is true when p is false and q is true, we conclude that these specifications are consistent because they are all true when p is false and q is true. We could come to the same conclusion by use of a truth table to examine the four possible assignments of truth values to p and q . ­