Fill in the blanks and state the property used.
If `x` and `y` are two integers, then `x + y` is also _______.

Options

A. an integer
Property used : Closure under subtraction
B. an integer
Property used : commutativity under addition
C. an integer
Property used : Closure under addition
D. an integer
Property used : associativity under addition

Answer

To solve the question, we need to fill in the blank and state the property used. The question states:

"If `x` and `y` are two integers, then `x + y` is also _______."

### Step-by-Step Solution:

1. **Understanding Integers**:
- Integers are whole numbers that can be positive, negative, or zero. Examples include -3, -2, -1, 0, 1, 2, 3, etc.

2. **Identifying the Property**:
- We need to determine what happens when we add two integers.

3. **Choosing Example Integers**:
- Let's take two integers as examples. Let `x = 5` and `y = 2`. Both are integers.

4. **Performing the Addition**:
- Now, we calculate `x + y`:
\[ x + y = 5 + 2 = 7 \]

5. **Checking the Result**:
- The result, `7`, is also an integer.

6. **Filling in the Blank**:
- Therefore, we can fill in the blank:
\[ \text{If } x \text{ and } y \text{ are two integers, then } x + y \text{ is also an integer.} \]

7. **Stating the Property Used**:
- The property used here is the **Closure Property of Addition** for integers, which states that the sum of any two integers is always an integer.

### Final Answer:
If `x` and `y` are two integers, then `x + y` is also **an integer**. The property used is the **Closure Property of Addition**.