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Consider the Statement  For all sets A and B,(AB)B=\text { For all sets } A \text { and } B , ( A - B ) \cap B = \emptyset \text {. }

question 7

Essay

Consider the statement  For all sets A and B,(AB)B=\text { For all sets } A \text { and } B , ( A - B ) \cap B = \emptyset \text {. }
The proof below is the beginning of a proof using the element method for proving that the
set equals the empty set. Complete the proof without using any of the set properties from
Theorem 6.2.2. Proof: Suppose the given statement is false. Then there exist sets AA and BB such that (A( A - B)BB ) \cap B \neq \emptyset . Thus there is an element xx in (AB)B( A - B ) \cap B . By definition of intersection,...


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