If U = {1, 2, ..., 18} and A = {x : x is a prime factor of 18}, what is n(P(A'))?
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Answer and explanation
Correct answer: 65536
The distinct prime factors of 18 are 2 and 3, so A = {2, 3} and n(A) = 2. The universal set U contains 18 elements, and therefore the complement A' contains 18 − 2 = 16 elements. For any finite set with k elements, its power set has 2^k elements. Thus n(P(A')) = 2^16 = 65,536, making option A correct.
Frequently asked questions
What is the correct answer to this question?
65536
Why is this the correct answer?
The distinct prime factors of 18 are 2 and 3, so A = {2, 3} and n(A) = 2. The universal set U contains 18 elements, and therefore the complement A' contains 18 − 2 = 16 elements. For any finite set with k elements, its power set has 2^k elements. Thus n(P(A')) = 2^16 = 65,536, making option A 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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