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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 $S_{1}\wedge S_{2}\wedge \dots \wedge S_{n}\neg S$ 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.

### 1 comment

Option 2. It should be valid, i.e. true for all conditions.

Ans:- option B

$S_1, S_2,\ldots ,S_n$  can be considered as premises and S is conclusion.  Argument $premises\implies conclusion$  is said to be valid(TRUR) if $S_1,S_2,S_3,\ldots,S_n \rightarrow S$  is valid. (False $\rightarrow$ or  True $\rightarrow$ True.)

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