If U = {1,2,3,4,5,6,7,8,9,10,11,12}, A = {1,2,3,4,5,6}, and B = {2,4,6,8,10,12}, what is Aᶜ ∩ B?
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Answer and explanation
Correct answer: {8,10,12}
The complement of A in U is Aᶜ = {7,8,9,10,11,12}. To find Aᶜ ∩ B, retain only the elements common to this complement and B. The elements of B are 2, 4, 6, 8, 10, and 12; among them, 8, 10, and 12 belong to Aᶜ. Hence Aᶜ ∩ B = {8,10,12}, making option A correct.
Frequently asked questions
What is the correct answer to this question?
{8,10,12}
Why is this the correct answer?
The complement of A in U is Aᶜ = {7,8,9,10,11,12}. To find Aᶜ ∩ B, retain only the elements common to this complement and B. The elements of B are 2, 4, 6, 8, 10, and 12; among them, 8, 10, and 12 belong to Aᶜ. Hence Aᶜ ∩ B = {8,10,12}, making option A correct.
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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