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Propositional truth tables:
There {X\t} is a substitution that replaces all occurances of variable X with a term representing an object t as:
By repeating this for all the quantifiers than we get a set of ground formulae in which we have to check that if the original sentence is true or false. But unfortunately, we don't have specified there that our domain Δ is finite - like in example we see that it may contain the natural numbers - but there may be a infinite number of sentences to check for a given model! So there may be also be an infinite number of models. And although we have a proper definition of model hence a proper semantics for first-order logic and we can't rely on having a finite number of models like we did where drawing propositional truth tables.
(1-x^2 ) (d^2 y)/?dx?^(2 ) -x dy/dx-4y=0
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kcl & kvl
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