1. Commutative: the result is the same if operands are commutated. $x + y$ is the same as $y + x.$ Assosicative: $x + y + z$ is the same as $(x + y) + z$ as $x + (y + z)$. It doesn't matter if you assigned an order (also: associate) to $(x+y)$ before $(y + z)$ and vice versa.
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