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Here are the correct designations for each equation based on the properties they represent:
1. **Commutative Property**
- **a ⋅ b = b ⋅
- **a + b = b +
2. **Associative Property**
- **a + (b + c) = (a + b) + c**
- **a ⋅ (b ⋅ c) = (a ⋅ b) ⋅ c**
You can drag or drop the equations to their respective areas based on these categorizations.