Question
Download Solution PDFConsider the following statements:
I. The set of all irrational numbers between \(\sqrt{12}\) and \(\sqrt{15}\) is an infinite set.
II. The set of all odd integers less than 1000 is a finite set.
Which of the statements given above is/are correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Properties of Irrational Numbers:
- Between any two irrational numbers, there are an infinite number of irrational numbers.
- The set of all irrational numbers between \( \sqrt{12} \) and \( \sqrt{15} \) is an infinite set.
Calculation:
Between any two irrational numbers, there are an infinite number of irrational numbers.
The set of all irrational numbers between \( \sqrt{12} \) and \( \sqrt{15} \) is an infinite set.
Also, the set of all odd integers less than 1000 is \( \{-5, -3, 1, 3, \dots, 999\} \), which is an infinite set.
Hence, Option (a) is correct.
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