Z and Z mod d/Subset no homomorphism/Exercise

Let ${}d\in \mathbb {N} _{\geq 2}$. We consider

${}\mathbb {Z} /(d)=\{0,1,\ldots ,d-1\}\,$

with the addition described in exercise. Show that the mapping

$\psi \colon \mathbb {Z} /(d)\longrightarrow \mathbb {Z} ,r\longmapsto r,$

is not a group homomorphism.

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