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3. Let $?:Z?Q$ be defined by $?(x)=[(x,1)]$. (a) Prove that $?$ is injective but not surjective. Proof: (b) Prove that if $x,y?Z$, thrn $?(x+y)=?(x)+?(y)and?(x?y)=?(x)??(y).$ Proof: (c) Suppose $x,y?Z$. Prove that $x?y$ if and only if $?(x)??(y)$. Proof:

3) i:Z?Qbe defined by i(x)=[(x,1)]a) Let, i(x)=i(y)implies [(x,1)]=[(y,1)]implies x=yTher