Which of the following sentences are statements? Give reasons for your answer `:`
The square of a number is an even number.

Answer

To determine whether the sentence "The square of a number is an even number" is a statement, we can follow these steps:

### Step 1: Understand what a statement is
A statement is a declarative sentence that is either true or false, but not both.

### Step 2: Analyze the given sentence
The sentence "The square of a number is an even number" is a general statement about the squares of numbers.

### Step 3: Determine the truth value of the statement
To assess the truth value, we can consider different cases:
- If we take an even number, for example, 2:
- The square of 2 is \(2^2 = 4\), which is even.
- If we take an odd number, for example, 3:
- The square of 3 is \(3^2 = 9\), which is odd.

### Step 4: Conclusion about the statement
Since the statement does not hold true for all numbers (it is true for even numbers but false for odd numbers), we conclude that the statement is false in general.

### Step 5: Final determination
Since the sentence is a declarative sentence that can be classified as either true or false, we can conclude that it is indeed a statement.

### Final Answer
The sentence "The square of a number is an even number" is a statement because it is a declarative sentence that can be evaluated as false.

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