If the universal set is U={1,2,3,...,10}, A={2,4,6,8,10}, and C=A^c, what is the value of C^c∩{1,2,3,4}?
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Answer and explanation
Correct answer: {2,4}
All complements are taken with respect to U. Since C=A^c, taking the complement again gives C^c=(A^c)^c=A, by the double-complement law. Therefore, C^c∩{1,2,3,4}=A∩{1,2,3,4}. The elements common to A={2,4,6,8,10} and the second set are 2 and 4, so the answer is {2,4}, option A.
Frequently asked questions
What is the correct answer to this question?
{2,4}
Why is this the correct answer?
All complements are taken with respect to U. Since C=A^c, taking the complement again gives C^c=(A^c)^c=A, by the double-complement law. Therefore, C^c∩{1,2,3,4}=A∩{1,2,3,4}. The elements common to A={2,4,6,8,10} and the second set are 2 and 4, so the answer is {2,4}, option A.
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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