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Precalculus Mathematics Homework Help
Analyzing a Quantified Statement: True or False?
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[QUOTE="andrewkirk, post: 5842793, member: 265790"] Some observations: [LIST] [*]In the antecedent you have used a ##z## that is a free variable (ie unquantified). Was that supposed to be ##x##? If it is a z then neither the original statement nor its negation has a truth value, as both contain a free variable and hence are not a sentence. [*]The 'simplified' version of the negated formula is a correct negation of the original formula you wrote, but the unsimplified one is not, because the first conjunct of the consequent should be ##z\notin \mathbb Z##, not ##z\in \mathbb Z## [*]For (b), you have written 2y where it should be 7y, if your rendition of the original formula is correct. Also, you have put an 'or' where there should be an 'and' [*]If we replace ##z## by ##x## in the antecedent of the original then your statement about (c) is correct. Otherwise both are indeterminate. [*]Can you give an example of a value of #x## that falsifies the original statement (after replacing the z in the antecedent by x), thereby proving its negation? [/LIST] [/QUOTE]
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Analyzing a Quantified Statement: True or False?
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