If U={1,2,3,4,5,6,7,8,9,10}, A={1,2,3,4,5}, and B={2,4,6,8,10}, how many elements are in A'∪B'?
Answer and explanation
Correct answer: 8
Use De Morgan’s law: A'∪B'=(A∩B)'. The common elements of A and B are {2,4}, so |A∩B|=2. Since U has 10 elements, the complement of this intersection has 10−2=8 elements. Directly, A'={6,7,8,9,10} and B'={1,3,5,7,9}; their union is {1,3,5,6,7,8,9,10}, which also contains eight elements. Thus option C is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
Use De Morgan’s law: A'∪B'=(A∩B)'. The common elements of A and B are {2,4}, so |A∩B|=2. Since U has 10 elements, the complement of this intersection has 10−2=8 elements. Directly, A'={6,7,8,9,10} and B'={1,3,5,7,9}; their union is {1,3,5,6,7,8,9,10}, which also contains eight elements. Thus option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
