Which of the following ia not a logical statement

Options

A. There are finitely many real numbers
B. The product of rational number is irrrational
C. Every square is a rectangle
D. She is a beautiful girl

Answer

To determine which of the given options is not a logical statement, we need to analyze each option and see if it can be classified as either true or false. A logical statement is one that has a definite truth value (either true or false).

### Step-by-Step Solution:

1. **Analyze Option 1: "There are finitely many real numbers."**
- The set of real numbers is infinite, ranging from negative infinity to positive infinity.
- Therefore, this statement is false.
- Since it has a truth value (false), it is a logical statement.

2. **Analyze Option 2: "The product of rational numbers is irrational."**
- A rational number is defined as a number that can be expressed as the quotient of two integers.
- For example, the product of \( \frac{5}{4} \) and \( \frac{3}{9} \) is \( \frac{15}{36} \), which simplifies to \( \frac{5}{12} \), a rational number.
- Therefore, this statement is false.
- Since it has a truth value (false), it is a logical statement.

3. **Analyze Option 3: "Every square is a rectangle."**
- A square is defined as a quadrilateral with all sides equal, which fits the definition of a rectangle (a quadrilateral with opposite sides equal).
- Thus, this statement is true.
- Since it has a truth value (true), it is a logical statement.

4. **Analyze Option 4: "She is a beautiful girl."**
- This statement is subjective and depends on personal opinion. It does not provide a definitive truth value because it lacks context.
- We cannot classify this statement as true or false without knowing who "she" refers to.
- Therefore, this statement is not a logical statement.

### Conclusion:
The option that is not a logical statement is **Option 4: "She is a beautiful girl."**

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