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(Solved): 3. Let :ZQ be defined by (x)=[(x,1)]. (a) Prove that is injective but not surjective. ...



3. Let \( \iota: \mathbb{Z} \rightarrow \mathbb{Q} \) be defined by \( \iota(x)=[(x, 1)] \).
(a) Prove that \( \iota \) is in

3. Let be defined by . (a) Prove that is injective but not surjective. Proof: (b) Prove that if , thrn Proof: (c) Suppose . Prove that if and only if . Proof:


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