The closure property under subtraction for Class 7 refers to whether the result of subtracting any two numbers within a specific set will always be within that same set. Specifically for integers, the closure property under subtraction holds true. This means that when you subtract any integer from another integer, the result will always be another integer.
Understanding Closure Property
The closure property is a fundamental concept in mathematics. It helps us understand how operations like addition, subtraction, multiplication, and division behave with different sets of numbers. The specific case here, closure under subtraction, focuses on whether a set remains 'closed' under subtraction.
Integers and Subtraction
The reference states:
The closure property of integers under addition and subtraction states that the sum or difference of any two integers will always be an integer. if p and q are any two integers, p + q and p − q will also be an integer. Example : 7 – 4 = 3; 7 + (−4) = 3; both are integers.
This clearly indicates that if we take two integers (represented by p and q), subtracting q from p (p - q) will result in another integer.
Examples
Here are some examples illustrating the closure property of integers under subtraction:
- Positive minus positive: 10 - 5 = 5 (All integers)
- Positive minus negative: 7 - (-3) = 7 + 3 = 10 (All integers)
- Negative minus positive: -4 - 2 = -6 (All integers)
- Negative minus negative: -5 - (-1) = -5 + 1 = -4 (All integers)
In all these cases, the result is always an integer.
Summary
| Operation | Result | Closure Property? |
|---|---|---|
| Integer - Integer | An Integer | Yes |
Key Takeaway
The set of integers is closed under subtraction. This means you will never find a case where subtracting one integer from another results in a number that is not an integer.
