Definition of an atomic sentence

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    Atomic Definition
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An atomic sentence is defined as a statement that contains no logical connectives, typically represented by capital letters like P, Q, B1, and B2. In contrast, a molecular sentence consists of one or more atomic sentences combined with logical connectives such as negation, conjunction, or disjunction. Examples of molecular sentences include expressions like ~P, (P & Q), and ~(B1 -> B2) & B3. Understanding these definitions is essential for grasping the fundamentals of propositional logic. This clarification on atomic and molecular sentences provides a foundational knowledge for further study in logic.
Matthias765
Can somebody please tell me what is the definition of an atomic sentence and the definition of a molecular sentence? Thanks

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Atomic sentences have no connectives (~, &, v, ->, <->), and are usually represented by capital letters, sometimes using subscripts:

P
Q
B1
B2
etc.

A molecular sentence is composed of one or more atomic sentences and one or more connectives:
~P
(P & Q)
(P v ~Q)
~(B1 -> B2) & B3
etc.

Do you need to know more than that?
 
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Thanks for telling me about atomic and molecular sentences, that's all I need to know for now.
 
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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