High School

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a. Express the quantified statement in an equivalent way, that is, in a way that has exactly the same meaning.

b. Write the negation of the quantified statement. (The negation should begin with "all," "some," or "no.")

Answer :

a. The original quantified statement can be expressed in an equivalent way as follows: "For every element x in a particular set, there exists a property P(x) that holds true." This means that each element in the set possesses the specific property P(x).


b. The negation of the quantified statement would be: "There exists an element x in the particular set such that the property P(x) does not hold true." In this case, the negation asserts that at least one element in the set does not possess the property P(x).

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