If U = {1, 2, 3, 4, 5, 6, 7}, A = {2, 5, 7}, and B = A', what is B'?
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Answer and explanation
Correct answer: {2, 5, 7}
Because B = A', taking the complement of B gives B' = (A')'. The double-complement law states that the complement of a complement is the original set, so (A')' = A. Hence B' = A = {2, 5, 7}. In fact, B itself is {1, 3, 4, 6}; that is why option B represents the single complement and not B'.
Frequently asked questions
What is the correct answer to this question?
{2, 5, 7}
Why is this the correct answer?
Because B = A', taking the complement of B gives B' = (A')'. The double-complement law states that the complement of a complement is the original set, so (A')' = A. Hence B' = A = {2, 5, 7}. In fact, B itself is {1, 3, 4, 6}; that is why option B represents the single complement and not B'.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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