Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, A = {2, 4, 6, 8, 10, 12}, and B = {3, 6, 9, 12}. What is Aᶜ ∩ Bᶜ?
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Answer and explanation
Correct answer: {1, 5, 7, 11}
By De Morgan’s law, Aᶜ ∩ Bᶜ = (A ∪ B)ᶜ. The union A ∪ B is {2, 3, 4, 6, 8, 9, 10, 12}. Removing these elements from the universal set U leaves {1, 5, 7, 11}. Therefore, Aᶜ ∩ Bᶜ = {1, 5, 7, 11}. Notice that elements such as 6 and 12 are excluded because they belong to both A and B.
Frequently asked questions
What is the correct answer to this question?
{1, 5, 7, 11}
Why is this the correct answer?
By De Morgan’s law, Aᶜ ∩ Bᶜ = (A ∪ B)ᶜ. The union A ∪ B is {2, 3, 4, 6, 8, 9, 10, 12}. Removing these elements from the universal set U leaves {1, 5, 7, 11}. Therefore, Aᶜ ∩ Bᶜ = {1, 5, 7, 11}. Notice that elements such as 6 and 12 are excluded because they belong to both A and B.
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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