For A = {x ∈ R : 0 < x < 1} and B = {x ∈ Q : 0 < x < 1}, choose the correct statement.
Answer and explanation
Correct answer: Both are infinite, but they are not equal
The interval (0, 1) contains infinitely many real numbers, so A is infinite. It also contains infinitely many rational numbers, such as 1/2, 1/3, 1/4, and so on, so B is infinite. However, A contains irrational numbers such as √2/2, while B contains only rational numbers. Therefore B is a proper subset of A, and the two sets are not equal.
Frequently asked questions
What is the correct answer to this question?
Both are infinite, but they are not equal
Why is this the correct answer?
The interval (0, 1) contains infinitely many real numbers, so A is infinite. It also contains infinitely many rational numbers, such as 1/2, 1/3, 1/4, and so on, so B is infinite. However, A contains irrational numbers such as √2/2, while B contains only rational numbers. Therefore B is a proper subset of A, and the two sets are not equal.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
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