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Set Theoryhard
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A student claims that for any sets AAA, BBB, CCC, the expression (A∪B)∖C(A \cup B) \setminus C(A∪B)∖C is equivalent to (A∖C)∪(B∖C)(A \setminus C) \cup (B \setminus C)(A∖C)∪(B∖C). Which of the following characteristic function identities would directly prove or disprove this claim?