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State the negations of the following quantified statements. (a) For every set A, A A =

Chapter 3, Problem 7

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QUESTION:

State the negations of the following quantified statements. (a) For every set A, A A = . (b) There exists a set A such that A A.

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QUESTION:

State the negations of the following quantified statements. (a) For every set A, A A = . (b) There exists a set A such that A A.

ANSWER:

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The negation of the quantified statement is also a quantified statement. An opposite quantifier applied to the open sentence will get the negation of the statement.

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