MHB Adjacency Matrix Problem and Alphabet Problem

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Could some please tell me if they think my answer for 1c and 3d of these questions I've done are right. thanks.View attachment 4393View attachment 4394
 

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These appear to be for credit. If so, it is against forum policy knowingly to help with such problems. Please PM if it is otherwise. Thread closed.
 

Thread 'Deductive proof in logic formal systems'

I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...
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