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Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set. The set A × Z+ where, A = {2, 3} (Check all that apply.) [] The set is countable. [] The set is countably infinite with one-to-one correspondence 1 ↔ (2,1), 2 ↔ (3,1), 3 ↔ (2,2), 4 ↔ (3,2),and so on. [] The set is countably infinite with one-to-one correspondence 0 ↔ (2,1),1 ↔ (3,1), 2 ↔ (2,2), 3 ↔ (3,2), and so on. [] The set is uncountable.

Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set. The set A × Z+ where, A = {2, 3} (Check all that apply.) [] The set is countable. [] The set is countably infinite with one-to-one correspondence 1 ↔ (2,1), 2 ↔ (3,1), 3 ↔ (2,2), 4 ↔ (3,2),and so on. [] The set is countably infinite with one-to-one correspondence 0 ↔ (2,1),1 ↔ (3,1), 2 ↔ (2,2), 3 ↔ (3,2), and so on. [] The set is uncountable.

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 15E: Let A=R0, the set of all nonzero real numbers, and consider the following relations on AA. Decide in...
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Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set.

The set A × Z+ where, A = {2, 3} (Check all that apply.)

[] The set is countable.

[] The set is countably infinite with one-to-one correspondence 1 ↔ (2,1), 2 ↔ (3,1), 3 ↔ (2,2), 4 ↔ (3,2),and so on.

[] The set is countably infinite with one-to-one correspondence 0 ↔ (2,1),1 ↔ (3,1), 2 ↔ (2,2), 3 ↔ (3,2), and so on.

[] The set is uncountable.

 

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