MHB Rewrite the following sentence as a formal proposition.

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The discussion focuses on rewriting a complex conditional statement about eating fruits as a formal proposition. The original statement involves three variables: eating apples (G), durians (B), and rambutans (P), with specific conditions linking them. A proposed formal representation is given as $$(G\to \neg B) \land (B\to \neg P) \land (P\to \neg G) \land (G\lor B\lor P).$$ This formulation captures the relationships and exclusions among the three fruits while ensuring that at least one is consumed. The conversation emphasizes clarity in translating informal language into formal logical expressions.
Henry R
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I have a question here. I hope I'm not doing anything wrong here. So, we go!

"If I eat apples, then I will not eat durian, and if I eat durians, then I will not eat rambutans, and if I eat rambutans, then I will not eat apples, but I will surely eat either apples, durians or rambutans."

Let G =" I eat apples" , B ="I eat durians" , P = "I eat rambutans".

I have to rewrite the sentences as a formal proposition. Can you guys give your opinion on how to solve this?
 
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Henry R said:
I have a question here. I hope I'm not doing anything wrong here. So, we go!

"If I eat apples, then I will not eat durian, and if I eat durians, then I will not eat rambutans, and if I eat rambutans, then I will not eat apples, but I will surely eat either apples, durians or rambutans."

Let G =" I eat apples" , B ="I eat durians" , P = "I eat rambutans".

I have to rewrite the sentences as a formal proposition. Can you guys give your opinion on how to solve this?

I would go with the following:
$$(G\to \neg B) \land (B\to \neg P) \land (P\to \neg G) \land (G\lor B\lor P).$$
 
Ackbach said:
I would go with the following:
$$(G\to \neg B) \land (B\to \neg P) \land (P\to \neg G) \land (G\lor B\lor P).$$

Good!
 

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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