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07-rules-of-inference

# Domain all dogs x px therefore phis dog pc 18 rules

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Unformatted text preview: ): x is cute. Domain: all dogs Determine the argument using P(x) x P(x). Domain: all dogs x P(x) Therefore, P(his dog). P(c) 18 Rules of inference for quantified statement Let s be any student. Argument: student s has taken calculus. Therefore, all student has taken calculus. P(s). Therefore, x P(x). (s is an arbitrary member of the domain.) premises true conclusion true P(s) x P(x) Universal generalization 19 Rules of inference for quantified statement (example) State which rule of inference is applied in the following argument. Let s be any student. Student s has a personal computer. Therefore, all student has a personal computer. Solution: Determine individual propositional function P(x): x has a personal computer. Domain: all students Determine the argument using P(x) P(s). Therefore, x P(x). P(s) Domain: all students x P(x) (s is an arbitrary element of the domain.) 20 Rules of inference for quantified statement (example) Show if x (P(x) Q(x)) is true then x P(x) true. (using direct technique) x Q(x) is Solution: Assume x (P...
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