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So pa is true and qa is true element a can be any

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Unformatted text preview: (x) Q(x)) is true. If a is in the domain then P(a) Q(a) is true. So, P(a) is true and Q(a) is true. Element a can be any element in the domain. So, x P(x) is true and x Q(x) is true. Thus, x P(x) x Q(x) is true. x P(x) P(a) P(a) x P(x) 21 Rules of inference for quantified statement Argument: There is a fish in the pool. Therefore, some fish c in the pool. x P(x). Therefore, P(c). (c is some member of the domain.) premises true conclusion true x P(x) P(c) Existential instantiation 22 Rules of inference for quantified statement (example) State which rule of inference is applied in the following argument. There is a person in the store. Therefore, some person c is in the store. Solution: Determine individual propositional function P(x): x is in the store. Domain: all people Determine the argument using P(x) x P(x). x P(x) Therefore, P(c). P(c) Domain: all people (c is some element of the domain.) 23 Rules of inference for quantified statement Argument: George is in the pool. Therefore, there is a person in the pool. P(c). The...
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