We can use propositional logic to find if the given system specifications are consistent or not.
Let p denotes "The diagnostic message is not stored in the
buffer." and q denotes "The diagnostic message is
not retransmitted." statements.
Then the list of propositions can be written as:
1. "The diagnostic message is not stored in the buffer or it is
not retransmitted." => p ∨ q
2. "The diagnostic message is stored in the buffer." =>
¬p
3. "If the diagnostic message is stored in the buffer, then it is
retransmitted." => ¬p→ ¬q.
We know that
p q (¬p → ¬q)
---------------------------
F F
T
F T F
T F T
T T T
When p is true and q is true, then p ∨ q is true, ¬p is
false and (¬p → ¬q) is true.
When p is true and q is false, then p ∨ q is true, ¬p is
false and (¬p → ¬q) is true.
When p is false and q is true, then p ∨ q is true, ¬p is
true and (¬p → ¬q) is false.
When p is false and q is false, then p ∨ q is false, ¬p is
true and (¬p → ¬q) is true.
So, the given system specifications are not consistent.
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