Question
Statement-1 (Assertion): The product of any two irrational numbers is an irrational number.
Statement-2 (Reason): There are two irrational numbers whose product is not an irrational 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 the example:
\[ \sqrt{2} \times \sqrt{2} = 2 \]
Both numbers are irrational, but their product 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)