If U = {1,2,3,4,5,6,7,8,9} and A = {x ∈ U : x is prime}, what is the complement Aᶜ with respect to U?
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Answer and explanation
Correct answer: {1,4,6,8,9}
The prime numbers in U are 2, 3, 5, and 7, because each has exactly two positive divisors. Thus A = {2,3,5,7}. The complement contains the remaining elements of U, namely {1,4,6,8,9}. Notice that 1 is neither prime nor composite, so it belongs to the complement. Therefore option B is correct.
Frequently asked questions
What is the correct answer to this question?
{1,4,6,8,9}
Why is this the correct answer?
The prime numbers in U are 2, 3, 5, and 7, because each has exactly two positive divisors. Thus A = {2,3,5,7}. The complement contains the remaining elements of U, namely {1,4,6,8,9}. Notice that 1 is neither prime nor composite, so it belongs to the complement. Therefore option B is 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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