Given U = {1, 2, 3, 4, 5} and A′ = {4, 5}, what is A?
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Answer and explanation
Correct answer: {1, 2, 3}
A set and its complement partition the universal set into two disjoint parts. Therefore, A is obtained by removing A′ from U: A = U \ A′. Removing 4 and 5 from {1, 2, 3, 4, 5} leaves {1, 2, 3}. Thus option A is correct. Notice that option B gives the complement itself, not the original set.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3}
Why is this the correct answer?
A set and its complement partition the universal set into two disjoint parts. Therefore, A is obtained by removing A′ from U: A = U \ A′. Removing 4 and 5 from {1, 2, 3, 4, 5} leaves {1, 2, 3}. Thus option A is correct. Notice that option B gives the complement itself, not the original set.
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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