If a and b are integers then ab is a rational number Check the validity of the statement

Answer

To determine the validity of the statement "If a and b are integers, then ab is a rational number," we can follow these steps:

### Step 1: Understand the Definitions
- **Integers**: The set of whole numbers that can be positive, negative, or zero (e.g., -2, -1, 0, 1, 2).
- **Rational Numbers**: A number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero (e.g., 1/2, -3/4, 5).

### Step 2: Analyze the Statement
We need to check if the product of two integers (ab) is always a rational number.

### Step 3: Calculate the Product of Two Integers
Let’s take two integers:
- Let \( a = 2 \) (an integer)
- Let \( b = 3 \) (another integer)

Now, calculate the product:
\[ ab = 2 \times 3 = 6 \]

### Step 4: Check if the Product is Rational
The number 6 can be expressed as:
\[ 6 = \frac{6}{1} \]
Since 6 can be expressed as a fraction where both the numerator (6) and the denominator (1) are integers, it is a rational number.

### Step 5: Generalize the Result
The product of any two integers \( a \) and \( b \) can be expressed as:
\[ ab = \frac{ab}{1} \]
This shows that the product \( ab \) is also a rational number because both \( ab \) (the product) and 1 (the denominator) are integers.

### Conclusion
Since we have shown that the product of any two integers is a rational number, the statement "If a and b are integers, then ab is a rational number" is valid.

### Final Answer
The statement is **true**.

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