What is the correct relation between the set of rational numbers (ℚ) and the set of real numbers (ℝ)?
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Answer and explanation
Correct answer: ℚ ⊆ ℝ
A rational number can be written in the form p/q, where p and q are integers and q is nonzero. Every such number lies on the real number line, so every element of ℚ is an element of ℝ; therefore ℚ ⊆ ℝ. The sets are not equal because irrational numbers such as √2 and π belong to ℝ but not to ℚ.
Frequently asked questions
What is the correct answer to this question?
ℚ ⊆ ℝ
Why is this the correct answer?
A rational number can be written in the form p/q, where p and q are integers and q is nonzero. Every such number lies on the real number line, so every element of ℚ is an element of ℝ; therefore ℚ ⊆ ℝ. The sets are not equal because irrational numbers such as √2 and π belong to ℝ but not to ℚ.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
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