Let $ O $ be the set of odd integers and consider the function $ \Gamma : \mathbb{Z} \to O $ defined by $\Gamma(n) = 2n - 3$. Show that $ \Gamma $ is onto, by (1) finding an element, say $ x $ of $\mathbb{Z}$ that gets sent to an arbitrary element $ y $ in $ O $ (make sure you show that your element does in fact get sent to $ y $) and then (2) prove that $ x $ is in fact an element of $\mathbb{Z}$.

Firstly, we define onto function (Surjective function). Let X and Y are two sets. Then f:X→Y is said…

[H] Let 0 be the set of odd integers and consider the function T: Z → 0 defined by r(n) = 2n – 3. Show that r is onto, by (1) finding an element, say x of Z that gets sent to an arbitrary element y in 0 (make sure you show that your element does in fact get sent to y) and then (2) prove that r is in fact an element of Z.

[H] Let 0 be the set of odd integers and consider the function T: Z → 0 defined by r(n) = 2n – 3. Show that r is onto, by (1) finding an element, say x of Z that gets sent to an arbitrary element y in 0 (make sure you show that your element does in fact get sent to y) and then (2) prove that r is in fact an element of Z.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let $ O $ be the set of odd integers and consider the function $ \Gamma : \mathbb{Z} \to O $ defined by $\Gamma(n) = 2n - 3$. Show that $ \Gamma $ is onto, by (1) finding an element, say $ x $ of $\mathbb{Z}$ that gets sent to an arbitrary element $ y $ in $ O $ (make sure you show that your element does in fact get sent to $ y $) and then (2) prove that $ x $ is in fact an element of $\mathbb{Z}$.

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