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N J 9. Consider the permutations f and g = = 5 2 1 3 4 set {1, 2, 3, 4, 5). Then go f = 1 2 3 4 5 1 5 4 3 2 = 10. The function f: Z→→ Z defined by f(x) 5a + 2 is surjective (onto). 3 154 2 I on the

N J 9. Consider the permutations f and g = = 5 2 1 3 4 set {1, 2, 3, 4, 5). Then go f = 1 2 3 4 5 1 5 4 3 2 = 10. The function f: Z→→ Z defined by f(x) 5a + 2 is surjective (onto). 3 154 2 I on the

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 12E: 12. (See Exercise 10 and 11.) If each is identified with in prove that . (This means that the...
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7. If II is a partition of a nonempty set A, then A/(A/II) is an equivalence relation on A. 8. Let R be an equivalence relation on A and let a, b € A. If [a]n[b], then aRb. 9. Consider the permutations f = 1 2 3 4 5 and = 5 2 1 3 4 1 2 3 4 5 31 5 4 2 on the set (1, 2, 3, 4, 5). Then go f = 1 2 3 4 5 1 5 4 3 2 10. The function f: Z → Z defined by f(a) = 5x + 2 is surjective (onto). I
Transcribed Image Text:7. If II is a partition of a nonempty set A, then A/(A/II) is an equivalence relation on A. 8. Let R be an equivalence relation on A and let a, b € A. If [a]n[b], then aRb. 9. Consider the permutations f = 1 2 3 4 5 and = 5 2 1 3 4 1 2 3 4 5 31 5 4 2 on the set (1, 2, 3, 4, 5). Then go f = 1 2 3 4 5 1 5 4 3 2 10. The function f: Z → Z defined by f(a) = 5x + 2 is surjective (onto). I
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