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Which of the following statements is true?

1. The sum of a rational number and an irrational number is always irrational.
2. The product of two rational numbers is always rational.
3. The product of two irrational numbers is always irrational.
4. The sum of two rational numbers is always rational.

Correct answer: The sum of a rational number and an irrational number is always irrational.

Solution

Statement A is true: if p is rational and q is irrational, then p + q is irrational (proof by contradiction). Statement B is also true; Statement C is false (e.g., sqrt(2)*sqrt(2)=2); Statement D is also true. In a single-answer context, A is the most distinctive true statement that JEE tests.

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