Question
Statement-1 (Assertion): The sum of any two irrational numbers is an irrational number.
Statement-2 (Reason): There are two irrational numbers whose sum is a rational number.
Options:
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) Statement-1 is false, Statement-2 is true.
Solution
Consider:
\[ \sqrt{2} + (-\sqrt{2}) = 0 \]
Here, both numbers are irrational, but their sum is rational.
So:
- Statement-1 is false
- Statement-2 is true
Statement-2 provides a counterexample, proving Statement-1 is incorrect.
Final Answer
✔ Correct option: (d)