Let U = {x : x is a positive integer less than 10} and A = {x : x² < 20}. What is A′?
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Answer and explanation
Correct answer: {5, 6, 7, 8, 9}
Because U consists of the positive integers less than 10, U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. The condition x² < 20 is true for x = 1, 2, 3, and 4, since 4² = 16, but false for x = 5 because 5² = 25. Thus A = {1, 2, 3, 4}, and its complement in U is {5, 6, 7, 8, 9}.
Frequently asked questions
What is the correct answer to this question?
{5, 6, 7, 8, 9}
Why is this the correct answer?
Because U consists of the positive integers less than 10, U = {1, 2, 3, 4, 5, 6, 7, 8, 9}. The condition x² < 20 is true for x = 1, 2, 3, and 4, since 4² = 16, but false for x = 5 because 5² = 25. Thus A = {1, 2, 3, 4}, and its complement in U is {5, 6, 7, 8, 9}.
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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