a. $$ \begin{array}{l}(a+b)+c= \ a+(b+c)\end{array} $$

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UpStudy AI · Accepted Answer

The expression you've provided represents the associative property of addition, which states that the way in which numbers are grouped in an addition operation does not change their sum.

To demonstrate this property step by step:

1. **Identify the expression**: 
   We have two expressions:
   - Left side: $$ (a + b) + c $$
   - Right side: $$ a + (b + c) $$

2. **Evaluate the left side**:
   - First, add $$ a $$ and $$ b $$:
     $$
     a + b = x \quad \text{(let's denote this sum as } x\text{)}
     $$
   - Now, add $$ x $$ to $$ c $$:
     $$
     x + c = (a + b) + c
     $$

3. **Evaluate the right side**:
   - First, add $$ b $$ and $$ c $$:
     $$
     b + c = y \quad \text{(let's denote this sum as } y\text{)}
     $$
   - Now, add $$ a $$ to $$ y $$:
     $$
     a + y = a + (b + c)
     $$

4. **Compare the results**:
   - We have:
     $$
     (a + b) + c = x + c
     $$
     $$
     a + (b + c) = a + y
     $$
   - Since $$ x = a + b $$ and $$ y = b + c $$, both expressions ultimately yield the same result.

Thus, we conclude that:
$$
(a + b) + c = a + (b + c)
$$

This confirms the associative property of addition.
The associative property of addition states that when adding three numbers, the way you group them doesn't change the sum. So, $$ (a + b) + c = a + (b + c) $$.

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