- #1

karush

Gold Member

MHB

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Determine which of the folllowing operations are

$\textit{Additive on $\mathbb{Z}$}$

$\textit{Subtraction on $\mathbb{N}$}$

$\textit{Division on $\mathbb{R}$}$

$\textit{Division on $\mathbb{Z}/\{0\}$}$

$\textit{Composition on $D_4$}$

$\textit{Composition on the set of rotations done on $D_4$}$

$\textit{Multiplication mod 6 on $\mathbb{Z}_6$}$

I know this

we are going thru this next but trying to some understanding on here first

much thanks ahead

*,***Associative***, or***Identity****Inverse**$\textit{Additive on $\mathbb{Z}$}$

$\textit{Subtraction on $\mathbb{N}$}$

$\textit{Division on $\mathbb{R}$}$

$\textit{Division on $\mathbb{Z}/\{0\}$}$

$\textit{Composition on $D_4$}$

$\textit{Composition on the set of rotations done on $D_4$}$

$\textit{Multiplication mod 6 on $\mathbb{Z}_6$}$

I know this

*: $a(bc)=(ab)c$***Associativity***: $\exists e \in G$ such that $ ae=ea=a, \forall a \in G$***Identity***: $\forall a \in G \ni ab =ba = c$***Inverse**we are going thru this next but trying to some understanding on here first

much thanks ahead

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