If U={1,2,3,4,5,6,7,8,9,10,11,12}, A={1,2,3,4,5,6}, and B={2,4,6,8,10,12}, how many elements does Aᶜ∪Bᶜ contain?
Advertisement
Answer and explanation
Correct answer: 9
Use De Morgan’s law: Aᶜ∪Bᶜ=(A∩B)ᶜ. The common elements of A and B are A∩B={2,4,6}, so the intersection has 3 elements. Since U has 12 elements, its complement contains 12−3=9 elements. Directly, the union of the two complements contains every element except 2, 4, and 6, confirming that the answer is 9.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
Use De Morgan’s law: Aᶜ∪Bᶜ=(A∩B)ᶜ. The common elements of A and B are A∩B={2,4,6}, so the intersection has 3 elements. Since U has 12 elements, its complement contains 12−3=9 elements. Directly, the union of the two complements contains every element except 2, 4, and 6, confirming that the answer is 9.
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.
Advertisement