If U = {2, 4, 6, 8, 10} and A = {2, 10}, what is (A')'?
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Answer and explanation
Correct answer: {2, 10}
All complements are taken with respect to U. First, A' = U \ A = {4, 6, 8}. Taking the complement again gives (A')' = U \ {4, 6, 8} = {2, 10}. Thus the double-complement law, (A')' = A, is verified. Option B is only the first complement, and option C is U itself, not the double complement.
Frequently asked questions
What is the correct answer to this question?
{2, 10}
Why is this the correct answer?
All complements are taken with respect to U. First, A' = U \ A = {4, 6, 8}. Taking the complement again gives (A')' = U \ {4, 6, 8} = {2, 10}. Thus the double-complement law, (A')' = A, is verified. Option B is only the first complement, and option C is U itself, not the double complement.
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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