If the absoulte errors in two physical quantites `A` and `B` are `a` and `b` respectively, then the absoulte error in the value of `A-B` is

Options

A. `b-a`
B. `aneb`
C. `a+b`
D. `a-b`

Explanation

To solve the problem of finding the absolute error in the difference of two physical quantities \( A \) and \( B \), given their absolute errors \( a \) and \( b \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Quantities and Their Errors**:
- Let \( A \) be a physical quantity with an absolute error \( a \).
- Let \( B \) be another physical quantity with an absolute error \( b \).

2. **Define the Expression**:
- We are interested in the expression \( X = A - B \).

3. **Understand Error Propagation**:
- When performing operations like addition or subtraction, the absolute errors of the quantities involved add up. This is a fundamental rule in error analysis.

4. **Apply the Error Propagation Rule**:
- The absolute error in the result \( X \) (which is \( A - B \)) is given by the sum of the absolute errors of \( A \) and \( B \).
- Therefore, the absolute error in \( X \) can be expressed as:
\[ \Delta X = \Delta A + \Delta B \]
- Substituting the known errors:
\[ \Delta X = a + b \]

5. **Conclusion**:
- The absolute error in the value of \( A - B \) is \( a + b \).

### Final Answer:
The absolute error in the value of \( A - B \) is \( a + b \).

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