Transcription of Quantifiers and Negation - University of Washington
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Quantifiers and Negation - University of Washington
Quantifiers and NegationFor all of you, there exists information about quantifiers often quantify a variable for a statement, or predicate, by claiming a statement holdsfor allvalues of thequantity or we saythere existsa quantity for which the statement holds (at least one). Notationally, we canwrite this in shorthand as follows: x A, P(x),which claims: for allxin the setA, the statementP(x) is true. x A, P(x),which claims: there exists at least onexin the setAsuch that the statementP(x) is are many equivalent way to express these quantifiers inEnglish. Here are a few examples:Universal Quantifier: Here are a few ways to say x N: For all natural numbersx,.. , For allx N,.. , For anyx N,.. , For everyx N,.. Existential Quantifier: Here are a few ways to say x N: There exists a natural numberxsuch that.
negation of the quantifiers is a quick exercise that doesn’t require the use of any sophisticated logic rules, you just ‘flip’ the quantifiers, then negate the statement (when you get to the statement then you will need logic rules to negate).
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