Which one of the following is true?
2011
Which one of the following is true?
- A.
R ∩ S = (R ∪ S) − [(R − S) ∪ (S − R)]
- B.
R ∪ S = (R ∩ S) − [(R − S) ∪ (S − R)]
- C.
R ∩ S = (R ∪ S) − [(R − S) ∩ (S − R)]
- D.
R ∩ S = (R ∪ S) ∪ (R − S)
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Correct answer: A
The correct set theory identity is R ∩ S = (R ∪ S) - ((R - S) ∪ (S - R)). The expression (R - S) ∪ (S - R) defines the symmetric difference, consisting of elements in exactly one set. Subtracting these from the union R ∪ S isolates the elements present in both sets, which is the definition of intersection.
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