Hw2 Problem 4

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Problem 4

Determine whether the binary operation $*$ defined on $\mathbb{Z}$ by letting $a*b=a-b$ is commutative. Is $*$ associative?


$*$ is not commutative because $1*2=1-2=-1$ while, $2*1=2-1=1$, and $1\not=-1$.

$*$ is not associative because $(1*2)*3=-1*3=-4$ while, $1*(2*3)=1*-1=2$, and $-4\not=2$.

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