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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.
Find the Boolean expression for logic circuit shown in Figure below and reduce it using Boolean algebra. Ans. Y = (AB)' + (A' + B)' = A' + B' + AB' by using Demorgan's Theorem. =
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Connectives - first-order logic: We can string predicates all together in a sentence by using connectives into the same way to conduct that we did for propositional logic. We
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