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slides03 - Predicate Logic CMSC 250 1 Quantification q q q...

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1 CMSC 250 Predicate Logic

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2 CMSC 250 Quantification 5 x There exists an x 2200 x For all x's Domain- the set where these subjects come from ( 5 x) [P(x)] there exists an x for which predicate p is true ( 2200 x) [P(x)] for all x, predicate p is true Notation: 5 x Z there exists an x in the integers 2200 x R for all x's in the reals
3 CMSC 250 Predicate translation A student of mine is wearing a blue shirt. Domain: all people P Quantification: There is at least one Predicates: "wearing a blue shirt" and "is my student" Let B(x) represent "x is wearing a blue shirt" Let S(x) represent "x is my student" (5 x P) [B(x) ^ S(x)] All good students are in class. Domain: all people P Quantification: All of them Predicates: "are in class" and "is a good student" Let C(x) represent "x is in class" Let G(x) represent “x is a good student" (2200 x P) [G(x) C(x)]

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4 CMSC 250 Establishing truth and falsity To show 5 statement is true, find an example. To show 5 statement is false, show it's false for every member of the domain. To show a 2200 statement is true, show it's true for every member of the domain. To 2200 statement is false, find a counterexample. [There are other methods!!!]
5 CMSC 250 Negation of quantified statements (there is a cat that can fly) some cats can’t fly?

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slides03 - Predicate Logic CMSC 250 1 Quantification q q q...

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