For any whole numbers a, b, c is it true that `(a+b)+c=a+(c+b)`? Give reasons.

Options

A. No, by associative and commutative laws of subtraction
B. Yes, by associative and commutative laws of multiplication
C. Yes, by associative and coummutative laws of addition
D. None of these

Answer

To determine whether the statement \((a + b) + c = a + (c + b)\) is true for any whole numbers \(a\), \(b\), and \(c\), we can use the properties of addition.

### Step-by-Step Solution:

1. **Understanding the Expression**:
We have two expressions:
- Left side: \((a + b) + c\)
- Right side: \(a + (c + b)\)

2. **Applying Associative Property**:
The associative property of addition states that the way in which numbers are grouped in addition does not change their sum. This means:
\[ (x + y) + z = x + (y + z) \]
for any whole numbers \(x\), \(y\), and \(z\).

3. **Rearranging the Left Side**:
Let's apply the associative property to the left side:
\[ (a + b) + c = a + (b + c) \]

4. **Rearranging the Right Side**:
Now, let's look at the right side:
\[ a + (c + b) \]
By the commutative property of addition, which states that \(x + y = y + x\), we can rearrange \(c + b\) to \(b + c\):
\[ a + (c + b) = a + (b + c) \]

5. **Comparing Both Sides**:
Now we have:
- Left side: \(a + (b + c)\)
- Right side: \(a + (b + c)\)

Since both sides are equal, we conclude:
\[ (a + b) + c = a + (c + b) \]

6. **Final Conclusion**:
Therefore, the statement \((a + b) + c = a + (c + b)\) is true for any whole numbers \(a\), \(b\), and \(c\).