Quantifiers and variables - propositional model, Computer Engineering

Quantifiers and Variables - propositional model:

There is one question is arrives that 'What do sentences containing variables mean?' In other way of words, how does a first-order model decide where such a sentence is true or false? Here the first step is to ensure that for the sentence does not contain any free variables, variables that are not bound by associated with a quantifier. So there strictly speaking that a first-order expression is not a sentence unless all the variables are bound there. Moreover, we usually suppose that if a variable is not explicitly bound then really it  is implicitly universally quantified. 

So now we look for the outermost quantifier in our sentence. Whether If this is ∀ X then we consider the truth of the sentence for every value X could take then the outermost quantifier is ?X we require to find just a single possible value of X. Just to make this more formal we can need a concept of substitution.

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