07-rules-of-inference

premises true conclusion true pc x px existential

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Unformatted text preview: refore, x P(x). (c is a particular member of the domain.) premises true conclusion true P(c) x P(x) Existential generalization 24 Rules of inference for quantified statement (example) State which rule of inference is applied in the following argument. His dog is playing in the park. Therefore, There is a dog playing in the park. Solution: Determine individual propositional function P(x): x is playing in the park. Domain: all dogs Determine the argument using P(x) P(his dog). P(c) Therefore, x P(x). x P(x) Domain: all dogs 25 Rules of inference for quantified statement (example) Show if x (P(x) Q(x)) is true, then x P(x) true. (using direct technique) Solution: Assume x (P(x) Q(x)) is true. Let a be some element of the domain, that P(a) Q(a) is true. So, P(a) is true and Q(a) is true. So, x P(x) is true and x Q(x) is true. Thus, x P(x) x Q(x) is true x Q(x) is x P(x) P(c) P(a) x P(x) 26 Rules of inference (example) Show the following argument is valid. Every one in this class has taken a course in co...
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