State whether the following statements are True or False :
The product of three odd numbers is odd.

Answer

To determine whether the statement "The product of three odd numbers is odd" is true or false, we can analyze the properties of odd numbers and perform a step-by-step verification.

### Step-by-Step Solution:

1. **Understanding Odd Numbers**:
- An odd number is defined as any integer that cannot be evenly divided by 2. This means when you divide an odd number by 2, there is always a remainder of 1.
- Examples of odd numbers include 1, 3, 5, 7, 9, etc.

**Hint**: Remember that odd numbers have a specific property related to division by 2.

2. **Multiplying Odd Numbers**:
- Let's take three odd numbers. For example, we can use 3, 5, and 7.
- The product of these numbers can be calculated as follows:
- First, multiply the first two odd numbers:
\[ 3 \times 5 = 15 \]
- Now, multiply the result by the third odd number:
\[ 15 \times 7 = 105 \]

**Hint**: When multiplying, keep track of the results step by step.

3. **Analyzing the Result**:
- The result of multiplying 3, 5, and 7 is 105, which is also an odd number.
- This pattern holds true for any three odd numbers.

4. **Generalizing the Result**:
- If we take any odd number \(a\), \(b\), and \(c\), we can express them in the form \(2n + 1\) where \(n\) is an integer.
- The product can be represented as:
\[ (2n_1 + 1)(2n_2 + 1)(2n_3 + 1) \]
- When you expand this product, you will find that it results in an odd number.

5. **Conclusion**:
- Since the product of any three odd numbers results in another odd number, we can conclude that the statement "The product of three odd numbers is odd" is true.

### Final Answer:
The statement is **True**.