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Consider | Consider |
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[[latex2( |
$ |
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where X is some set of premises and y is the conclusion. This simply means that the conjuction of all the premises entail the conclusion. We say that [[latex2($X \models y$)]] if and only if all the models of [[latex2($X$)]] are models of [[latex2($y$)]]. | where $X$ represents some set of premises and y represents the conclusion. This simply means that the conjuction of all the premises entails the conclusion. We say that $$X \models y$$ if and only if all the models of $$X$$ are models of |
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To show [[latex2( |
To show |
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We call a tautology of the form [[latex2( |
In predicate calculus, we use |
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In predicate calculus, we often times use [[latex2( |
where (FirstOrderMathematicalLogicAngeloMargaris) |
Logical Implication or Entailment
Consider
where $X$ represents some set of premises and y represents the conclusion. This simply means that the conjuction of all the premises entails the conclusion. We say that
To show
In predicate calculus, we use
where
(FirstOrderMathematicalLogicAngeloMargaris)
See LogicNotes
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