If U = {1,2,...,15}, A = {1,5,9,13}, and B = {2,5,8,11,14}, what is (A ∩ B)′?
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Answer and explanation
Correct answer: {1,2,3,4,6,7,8,9,10,11,12,13,14,15}
The only common element of A and B is 5, so A ∩ B = {5}. The complement is taken relative to U, which contains all integers from 1 through 15. Removing 5 from U gives (A ∩ B)′ = {1,2,3,4,6,7,8,9,10,11,12,13,14,15}. Thus option A is correct; option C represents A ∪ B.
Frequently asked questions
What is the correct answer to this question?
{1,2,3,4,6,7,8,9,10,11,12,13,14,15}
Why is this the correct answer?
The only common element of A and B is 5, so A ∩ B = {5}. The complement is taken relative to U, which contains all integers from 1 through 15. Removing 5 from U gives (A ∩ B)′ = {1,2,3,4,6,7,8,9,10,11,12,13,14,15}. Thus option A is correct; option C represents A ∪ 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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