If U={1,2,...,12}, A={2,4,6,8,10,12}, and B={3,6,9,12}, how many elements are in (A∪B)'?
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Answer and explanation
Correct answer: 4
The union contains every element appearing in A or B: A∪B={2,3,4,6,8,9,10,12}. It has 8 elements. Since the universal set U has 12 elements, its complement has 12−8=4 elements, namely {1,5,7,11}. The same result follows from inclusion–exclusion: n(A∪B)=6+4−2=8 because 6 and 12 are counted in both sets.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The union contains every element appearing in A or B: A∪B={2,3,4,6,8,9,10,12}. It has 8 elements. Since the universal set U has 12 elements, its complement has 12−8=4 elements, namely {1,5,7,11}. The same result follows from inclusion–exclusion: n(A∪B)=6+4−2=8 because 6 and 12 are counted in both sets.
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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