If A is a finite set, B is a countable set, and An B = 0, prove that AU B is countable by finding a bijection h : N→ AU B. Is the result still true if the hypothesis AN B = Ø is removed? (Hint: It may help to think first about the special case where A has one element, say A = {a}. There is a bijection g : N → B. Find a bijection h : N → {a} UB. If B = {x, y,z,...}, think of An B as {a, x, y,z,...}, so a goes to the front of the list.) %3D

If A is a finite set, B is a countable set, and An B = 0, prove that AU B is countable by finding a bijection h : N→ AU B. Is the result still true if the hypothesis AN B = Ø is removed? (Hint: It may help to think first about the special case where A has one element, say A = {a}. There is a bijection g : N → B. Find a bijection h : N → {a} UB. If B = {x, y,z,...}, think of An B as {a, x, y,z,...}, so a goes to the front of the list.) %3D

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 34E: 34. If is an ideal of prove that the set is an ideal of . The set is called the annihilator of the...

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