Question

Statement 1: The sum of a rational number and an irrational number may or may not be irrational.

Statement 2: The difference of two irrational numbers may or may not be irrational.

• A. Both statement 1 and statement 2 are true.
• B. Statement 1 is true, while statement 2 is false.
• C. Statement 1 is false, while statement 2 is true.
• D. Both statement 1 and statement 2 are false.

Answer 1

The correct option is C Statement 1 is false, while statement 2 is true.

The sum of a rational and an irrational number is always irrational.
Ex: 3 is a rational number, $\pi$ is an irrational number, and 3 + $\pi$ is also an irrational number.
This is true for any pair of a rational and an irrational number.

The difference of two irrational numbers may or may not be irrational.
Ex: $\sqrt{5}-\sqrt{3}$ is an irrational number, but $\sqrt{5}-\sqrt{5}=0$ is a rational number.

Hence, statement 1 is false, while statement 2 is true.