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For all sets A, B, and C. Assuming each is a subset of a universal set U

For all sets A, B, and C. Assuming each is a subset of a universal set U
a)Is the following true? (A-B)∩ (C-B) = A- (B ∪C)
b)Find a counterstatement to (a)

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Michael F. | Mathematics TutorMathematics Tutor
4.7 4.7 (6 lesson ratings) (6)
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For any set A let A'=complement of A.  Definition: A-B=A∩B' . De Morgan's Law: (B∪C)'=B'∩C'
Now we begin
(A-B)∩C-B=A∩B'∩C∩B'=A∩C∩B'=A∩B'∩C
A-(B ∪C)=A∩(B ∪C)'=A∩B'∩C'
The two sets are disjoint! One is a subset of C, the other of C'