Closure propertry does not hold in integers for

Options

A. multiplication
B. division
C. addition
D. subtraction

Answer

To determine which arithmetic operation does not satisfy the closure property for integers, we will analyze each operation: addition, subtraction, multiplication, and division.

### Step-by-Step Solution:

1. **Understanding Closure Property**:
- The closure property states that if you perform an operation on two integers, the result must also be an integer.

2. **Testing Addition**:
- Let's take two integers, for example, \(3\) and \(5\).
- When we add them:
\[ 3 + 5 = 8 \]
- Since \(8\) is also an integer, addition satisfies the closure property.

3. **Testing Subtraction**:
- Now, let's take two integers, for example, \(5\) and \(3\).
- When we subtract them:
\[ 5 - 3 = 2 \]
- Since \(2\) is also an integer, subtraction satisfies the closure property.

4. **Testing Multiplication**:
- Next, we will test multiplication with two integers, for example, \(4\) and \(2\).
- When we multiply them:
\[ 4 \times 2 = 8 \]
- Since \(8\) is also an integer, multiplication satisfies the closure property.

5. **Testing Division**:
- Finally, we will test division with two integers, for example, \(8\) and \(4\).
- When we divide them:
\[ 8 \div 4 = 2 \]
- Since \(2\) is also an integer, this example satisfies the closure property.
- Now, let's take another example with \(7\) and \(2\):
\[ 7 \div 2 = 3.5 \]
- Since \(3.5\) is not an integer, division does not satisfy the closure property.

### Conclusion:
The operation that does not satisfy the closure property for integers is **division**.

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