If U = {1, 2, 3, 4, 5, 6, 7} and Aᶜ = {1, 7}, what is A?
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Answer and explanation
Correct answer: {2, 3, 4, 5, 6}
The complement Aᶜ contains the elements of the universal set U that are not in A. Therefore, A is obtained by removing the elements of Aᶜ from U. Removing 1 and 7 from {1, 2, 3, 4, 5, 6, 7} leaves A = {2, 3, 4, 5, 6}. Hence option A is correct. This also illustrates the identity (Aᶜ)ᶜ = A.
Frequently asked questions
What is the correct answer to this question?
{2, 3, 4, 5, 6}
Why is this the correct answer?
The complement Aᶜ contains the elements of the universal set U that are not in A. Therefore, A is obtained by removing the elements of Aᶜ from U. Removing 1 and 7 from {1, 2, 3, 4, 5, 6, 7} leaves A = {2, 3, 4, 5, 6}. Hence option A is correct. This also illustrates the identity (Aᶜ)ᶜ = A.
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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