Let A and B be sets and let Ac and Bc denote the complements of the sets A and…
1996
Let A and B be sets and let Ac and Bc denote the complements of the sets A and B. The set (A−B) ∪ (B−A) ∪ (A ∩ B) is equal to
- A.
A ∪ B
- B.
Ac ∪ Bc
- C.
A ∩ B
- D.
Ac ∩ Bc
Attempted by 67 students.
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Correct answer: A
(a-b) contains elements that are in a but not in b. (b-a) contains elements that are in b but not in a. a intersection b contains the common elements.
these three regions are disjoint and together make exactly all elements that are in a or in b. hence their union is a union b.
therefore, (a-b) union (b-a) union (a intersection b) = a union b, so option 1 is correct.