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match the universal quantification on the left with a domain for the variable x on the right that will make the statement true.

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User Helpful
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Final answer:

In mathematics, a universal quantification statement states that a certain property holds for all elements within a domain. It can be rephrased as a conditional, suggesting a sufficient condition. To validate such a statement, a domain should be chosen where no counterexamples exist.

Step-by-step explanation:

The student's question involves matching a universal quantification statement with a domain for the variable that would make the statement true. In logic and mathematics, a universal quantification of a property over a domain asserts that the property holds for all members of the domain. These types of statements can often be rephrased as conditionals, where the universal statement "All A are B" can be seen as "If something is A, then it is necessarily B". Thus, it's a statement of sufficiency, stating that being A is sufficient for being B.

When trying to match these statements with a domain, it is crucial to pick a domain where the property will indeed hold for all its members. For instance, if we have a universal statement like "All x are even", a correct domain might be the set of all integers multiples of 2, as this guarantees the truth of the statement. If even a single counterexample can be found within the proposed domain, however, the universal statement is false.

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User Zerobandwidth
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