If U={1,2,3,4,5,6,7}, A={1,2,4}, and B={2,4,6}, what is (A∩B)'?
Answer and explanation
Correct answer: {1,3,5,6,7}
First find the intersection: A∩B contains the elements common to both sets, so A∩B={2,4}. The prime symbol denotes complement relative to the stated universal set U. Therefore (A∩B)'=U\(A∩B)={1,2,3,4,5,6,7}\{2,4}={1,3,5,6,7}. Option B is only the intersection, not its complement; the other options omit elements that must remain in the complement.
Frequently asked questions
What is the correct answer to this question?
{1,3,5,6,7}
Why is this the correct answer?
First find the intersection: A∩B contains the elements common to both sets, so A∩B={2,4}. The prime symbol denotes complement relative to the stated universal set U. Therefore (A∩B)'=U\(A∩B)={1,2,3,4,5,6,7}\{2,4}={1,3,5,6,7}. Option B is only the intersection, not its complement; the other options omit elements that must remain in the complement.
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.
