Find Whether the Following Statements are True or False
Solution:
(i) Every real number is either rational or irrational.
All real numbers can be classified into two categories: rational and irrational.
Answer: True
(ii) \( \sqrt{2} \) is an irrational number.
\( \sqrt{2} \) cannot be expressed as \( \frac{p}{q} \) and its decimal expansion is non-terminating and non-repeating.
Answer: True
(iii) Irrational numbers cannot be represented by points on the number line.
Every real number (including irrational numbers) corresponds to a point on the number line.
Answer: False
Final Answers:
- (i) True
- (ii) True
- (iii) False