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a. Define F: Z → Z by the rule F(n) = 2-3n, for all integers n. (1) Is F one-to-one? Prove or give a counterexample. (ii) Is F onto? Prove or give a counterexample.

a. Define F: Z → Z by the rule F(n) = 2-3n, for all integers n. (1) Is F one-to-one? Prove or give a counterexample. (ii) Is F onto? Prove or give a counterexample.

Advanced Engineering Mathematics
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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How do you solve #12 parts I, ii?
(i) Is f one-to-one? Prove or give a (ii) Is fonto? Prove or give a counterexample. b. Let 2Z denote the set of all even integers. That is, 2Z = {n € Zn = 2k, for some integer k}. Define h: Z→ 2Z by the rule h (n) = 2n, for all integers n. Is h onto? Prove or give a counterexample. H 11. a. Define g: Z→ Z by the rule g(n) = 4n - 5, for all integers n. (i) Is g one-to-one? Prove or give a counterexample. (ii) Is g onto? Prove or give a counterexample. b. Define G: R→ R by the rule G(x) = 4x - 5 for all real numbers x. Is G onto? Prove or give a counterex- ample. 12. a. Define F: Z→ Z by the rule F(n) = 2-3n, for all integers n. (i) Is F one-to-one? Prove or give a counterexample. (ii) Is F onto? Prove or give a counterexample. b. Define G: R→ R by the rule G(x) = 2 - 3x for all real numbers x. Is G onto? Prove or give a counterexample. H 21. D с 22. 23. a 24.
Transcribed Image Text:(i) Is f one-to-one? Prove or give a (ii) Is fonto? Prove or give a counterexample. b. Let 2Z denote the set of all even integers. That is, 2Z = {n € Zn = 2k, for some integer k}. Define h: Z→ 2Z by the rule h (n) = 2n, for all integers n. Is h onto? Prove or give a counterexample. H 11. a. Define g: Z→ Z by the rule g(n) = 4n - 5, for all integers n. (i) Is g one-to-one? Prove or give a counterexample. (ii) Is g onto? Prove or give a counterexample. b. Define G: R→ R by the rule G(x) = 4x - 5 for all real numbers x. Is G onto? Prove or give a counterex- ample. 12. a. Define F: Z→ Z by the rule F(n) = 2-3n, for all integers n. (i) Is F one-to-one? Prove or give a counterexample. (ii) Is F onto? Prove or give a counterexample. b. Define G: R→ R by the rule G(x) = 2 - 3x for all real numbers x. Is G onto? Prove or give a counterexample. H 21. D с 22. 23. a 24.
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