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GO Classes CS 2025 | Weekly Quiz 2 | Propositional Logic | Question: 6

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Which of the following statements is true?

  1. The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2} \wedge \dots \wedge S_{n}\rightarrow S$ is satisfiable.
  2. The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\rightarrow S$ is valid.
  3. The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\wedge S$ is consistent.
  4. The sentence $S$ is a logical consequence of $S_{1},\dots,S_{n}$ if and only if $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\wedge S$ is inconsistent.
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The sentence $S$ is a logical consequence of $S_{1}, ... S_{n}$ if and only if $S_{1} \wedge S_{2} ... \wedge S_{n} \rightarrow S$ is Tautology or Valid, hence option B is correct.

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Logical consequence is a concept which describes the relationship between statements that hold TRUE/VALID when one statement logically follows from one or more statements (Source: Wikipedia)
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all tautologies are valid but all valid are not tautology
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