If U={1,2,3,...,11}, A={1,4,7,10}, and B={2,4,6,8,10}, what is A^c ∩ B^c?
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Answer and explanation
Correct answer: {3,5,9,11}
The complement A^c contains the elements of U that are not in A, while B^c contains the elements of U that are not in B. By De Morgan’s law, A^c ∩ B^c = (A ∪ B)^c. Here, A ∪ B = {1,2,4,6,7,8,10}. Removing these elements from U={1,2,3,...,11} leaves {3,5,9,11}. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
{3,5,9,11}
Why is this the correct answer?
The complement A^c contains the elements of U that are not in A, while B^c contains the elements of U that are not in B. By De Morgan’s law, A^c ∩ B^c = (A ∪ B)^c. Here, A ∪ B = {1,2,4,6,7,8,10}. Removing these elements from U={1,2,3,...,11} leaves {3,5,9,11}. Therefore, option A is 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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