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Bot GPT 4-o mini The Associative Property of Addition states that how numbers are grouped in addition does not change their sum. This can be expressed as \( (a + b) + c = a + (b + c) \).
Looking at the options you've provided:
1. **\( m \cdot (x \cdot y) = (m \cdot x) \cdot y \)** - This demonstrates the Associative Property of Multiplication, not addition.
2. **\( y - (x + 1) = (y - x) + 1 \)** - This is not a demonstration of the Associative Property of Addition; it involves subtraction and does not group terms that represent addition.
3. **\( x \cdot (y + z) = (x \cdot y) + z \)** - This depicts a multiplication operation, and thus does not represent the Associative Property of Addition.
4. **\( (x + y) + z + r = x(y + z) + r \)** - This expression is incorrect since it does not represent a valid form of addition or the Associative Property of Addition.
None of the provided options correctly demonstrates the Associative Property of Addition as they all involve either multiplication or incorrect representations of addition and subtraction.
To summarize, the correct expression for the Associative Property of Addition would look like \( (a + b) + c = a + (b + c) \).