If U = {x ∈ N : 1 ≤ x ≤ 12} and A = {x ∈ U : x is prime}, what is |P(A')|?
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Answer and explanation
Correct answer: 128
The natural numbers from 1 through 12 are the elements of U. The primes in this interval are 2, 3, 5, 7, and 11, so A has 5 elements. Therefore, its complement A' has 12 − 5 = 7 elements. The power set of a 7-element set has 2^7 = 128 members. Note that 1 is not prime. Hence option B is correct.
Frequently asked questions
What is the correct answer to this question?
128
Why is this the correct answer?
The natural numbers from 1 through 12 are the elements of U. The primes in this interval are 2, 3, 5, 7, and 11, so A has 5 elements. Therefore, its complement A' has 12 − 5 = 7 elements. The power set of a 7-element set has 2^7 = 128 members. Note that 1 is not prime. 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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