If U={1,2,3,...,12} and A={3,6,9,12}, how many elements are in A^c ∪ {6,12}?
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Answer and explanation
Correct answer: 10
The complement A^c contains all elements of U that are not in A. Thus, A^c={1,2,4,5,7,8,10,11}, which has 8 elements. The elements 6 and 12 belong to A, so neither is already in A^c. Adding both of them to A^c gives {1,2,4,5,6,7,8,10,11,12}, containing 10 elements. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
10
Why is this the correct answer?
The complement A^c contains all elements of U that are not in A. Thus, A^c={1,2,4,5,7,8,10,11}, which has 8 elements. The elements 6 and 12 belong to A, so neither is already in A^c. Adding both of them to A^c gives {1,2,4,5,6,7,8,10,11,12}, containing 10 elements. Therefore, option A is correct.
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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