Let U = {x : x ∈ N and x ≤ 50}, and let A be the set of multiples of 10 in U. What is |P(A')|, where A' is the complement of A in U?
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Answer and explanation
Correct answer: 2^45
The natural numbers in U are 1 through 50, so U has 50 elements. The multiples of 10 are {10, 20, 30, 40, 50}, giving |A| = 5. Therefore, the complement A' has 50 − 5 = 45 elements. A set with 45 elements has 2^45 subsets, so |P(A')| = 2^45. Hence, option B is correct.
Frequently asked questions
What is the correct answer to this question?
2^45
Why is this the correct answer?
The natural numbers in U are 1 through 50, so U has 50 elements. The multiples of 10 are {10, 20, 30, 40, 50}, giving |A| = 5. Therefore, the complement A' has 50 − 5 = 45 elements. A set with 45 elements has 2^45 subsets, so |P(A')| = 2^45. Hence, option B 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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