If A has n elements and |P(A)| = |P(A')|, where A ⊆ U and |U| = 12, what is the value of n?
Answer and explanation
Correct answer: 6
If A has n elements, then its power set has 2^n elements. Since U has 12 elements, the complement A' has 12 - n elements, and therefore P(A') has 2^(12-n) elements. The given equality becomes 2^n = 2^(12-n). Equal powers of the same base have equal exponents, so n = 12 - n. Thus 2n = 12 and n = 6. Therefore, option C is correct.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
If A has n elements, then its power set has 2^n elements. Since U has 12 elements, the complement A' has 12 - n elements, and therefore P(A') has 2^(12-n) elements. The given equality becomes 2^n = 2^(12-n). Equal powers of the same base have equal exponents, so n = 12 - n. Thus 2n = 12 and n = 6. Therefore, option C is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
