Question

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

Answer 1

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.