If U = {1, 2, 3, 4, 5} and Aᶜ = {2, 5}, what is A ∪ Aᶜ?
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Answer and explanation
Correct answer: U
A set together with its complement covers every element of the universal set. Here Aᶜ = {2, 5}, so A = U − Aᶜ = {1, 3, 4}. Taking the union gives {1, 3, 4} ∪ {2, 5} = {1, 2, 3, 4, 5} = U. Thus the correct answer is option A. The other listed sets represent only one set or the empty set, not the complete union.
Frequently asked questions
What is the correct answer to this question?
U
Why is this the correct answer?
A set together with its complement covers every element of the universal set. Here Aᶜ = {2, 5}, so A = U − Aᶜ = {1, 3, 4}. Taking the union gives {1, 3, 4} ∪ {2, 5} = {1, 2, 3, 4, 5} = U. Thus the correct answer is option A. The other listed sets represent only one set or the empty set, not the complete union.
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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