It is known that if `a + b = 10`, then `a + b - c = 10 - c`. State the Euclid's axiom that best illustrates this statement.

Options

A. If equals be subtracted from equals, the remainders are equal.
B. Things which are halves of the same thing are equal to one other.
C. The whole is greater than the part.
D. None of these

Answer

To solve the question, we need to identify the Euclid's axiom that best illustrates the statement given: "If \( a + b = 10 \), then \( a + b - c = 10 - c \)."

### Step-by-Step Solution:

1. **Understanding the Given Statement**:
We have the equation \( a + b = 10 \). This means that the sum of \( a \) and \( b \) is equal to 10.

2. **Manipulating the Equation**:
From the equation \( a + b = 10 \), we can subtract \( c \) from both sides of the equation. This gives us:
\[ a + b - c = 10 - c \]
This shows that if we take away \( c \) from both sides, the equality still holds.

3. **Identifying the Axiom**:
The axiom that best illustrates this property is known as the "Axiom of Equality." This axiom states that if two quantities are equal, then subtracting the same quantity from both sides will yield equal results.

In Euclid's terms, this can be summarized as:
- "Things which are equal to the same thing are equal to one another."

4. **Conclusion**:
Therefore, the Euclid's axiom that best illustrates the statement is that if \( a + b = 10 \), then subtracting \( c \) from both sides maintains the equality, which can be expressed as:
- "If \( a = b \) and \( b = c \), then \( a = c \)."