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Prove or disprove: Let S be a nonempty set. For every proper subset A of S, there exists

Chapter 3, Problem 16

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QUESTION:

Prove or disprove: Let S be a nonempty set. For every proper subset A of S, there exists a nonempty subset B of S such that A B = S and A B = .

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QUESTION:

Prove or disprove: Let S be a nonempty set. For every proper subset A of S, there exists a nonempty subset B of S such that A B = S and A B = .

ANSWER:

Step 1 of 2

A quantified statement is disproved by using the counterexample method. The direct proof or proof by contrapositive is used for proving a statement is true.

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