If U = {1, 2, ..., 16}, A = {1, 3, 5, 7, 9, 11, 13, 15}, and B = {1, 2, 3, 5, 8, 13}, what is A' ∩ B'?
Answer and explanation
Correct answer: {4, 6, 10, 12, 14, 16}
The set A contains all odd numbers from 1 through 15, so A' within U is {2, 4, 6, 8, 10, 12, 14, 16}. To obtain A' ∩ B', remove from this list the elements that occur in B. The only such element is 8. Therefore the result is {2, 4, 6, 10, 12, 14, 16}; however, because 2 is in B, it must also be removed. Thus A' ∩ B' = {4, 6, 10, 12, 14, 16}, option A.
Frequently asked questions
What is the correct answer to this question?
{4, 6, 10, 12, 14, 16}
Why is this the correct answer?
The set A contains all odd numbers from 1 through 15, so A' within U is {2, 4, 6, 8, 10, 12, 14, 16}. To obtain A' ∩ B', remove from this list the elements that occur in B. The only such element is 8. Therefore the result is {2, 4, 6, 10, 12, 14, 16}; however, because 2 is in B, it must also be removed. Thus A' ∩ B' = {4, 6, 10, 12, 14, 16}, option 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.
