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Is possible to have a false conclusion given that all its premises are true?

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    NO. Valid argument means that "it impossible for the premises to be true and the conclusion nevertheless to be false." – Mauro ALLEGRANZA Sep 3 '18 at 8:56
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    You have remove the "valid" requirement: now an "argument" is a collection of sentences whatever. So, you can do whatever you want... – Mauro ALLEGRANZA Sep 3 '18 at 9:19
  • If you have an uncountable number of premises, you might be able to conjure up some sort of Axiom of Choice weirdness. In that case, the conclusion would be unprovable, not false. – barrycarter Sep 4 '18 at 20:45
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It is possible for an argument to have a false conclusion and also all true premises. An example is: Today is a weekday or a weekend, so you live on Mars. However, this situation is not possible when the argument is logically valid. Indeed, that is the definition of logical validity: that this situation is impossible.

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