State true or false:
(i) Negative of an irrational number is irrational .
(ii) The product of a non- zero rational number and an irrational number is a rational number.

Answer

To solve the question, we need to evaluate two statements regarding rational and irrational numbers and determine if they are true or false.

### Step-by-Step Solution:

1. **Evaluate the first statement: "Negative of an irrational number is irrational."**
- Let’s take an example of an irrational number, such as √2. The negative of √2 is -√2.
- We know that √2 is irrational. The property of irrational numbers states that if a number is irrational, then its negative will also be irrational.
- Therefore, the first statement is **True**.

2. **Evaluate the second statement: "The product of a non-zero rational number and an irrational number is a rational number."**
- Let’s take a non-zero rational number, for example, 2 (which can be expressed as 2/1).
- Now, let’s multiply it by an irrational number, such as √3. The product is 2 * √3.
- We need to determine whether 2 * √3 is rational or irrational.
- The product of a non-zero rational number and an irrational number is always irrational. Thus, 2 * √3 is irrational.
- Therefore, the second statement is **False**.

### Final Answers:
- (i) True
- (ii) False