If U = {1,2,...,14}, A = {2,4,6,8,10,12,14}, and B = {1,3,5,7,9,11,13}, what is true about P(A') = P(B)?
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Answer and explanation
Correct answer: It is true because A' = B
The universal set contains the numbers 1 through 14. A contains all the even numbers in U, so its complement A' contains precisely the odd numbers {1,3,5,7,9,11,13}. This is exactly B. Equal sets have identical collections of subsets, so P(A') = P(B). Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
It is true because A' = B
Why is this the correct answer?
The universal set contains the numbers 1 through 14. A contains all the even numbers in U, so its complement A' contains precisely the odd numbers {1,3,5,7,9,11,13}. This is exactly B. Equal sets have identical collections of subsets, so P(A') = P(B). Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
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