Discrete math question: Determine whether each of these sets is finite, countabl

Question

Discrete math question: 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.

b) The odd negative integers The set is countably infinite The set is finite. O The set is countably infinite with one-to-one correspondence !-1 2-3·3m-5 4-7 and so on. O The set is countably infinite with one-to-one correspondence !-1.2-2·3m-3, 4-4, and so on. The one-to-one correspondence is given by n-(2n-1). O The one-to-one correspondence is given by n -(n-1)

Explanation / Answer

b) The set of odd integers

The set is countably infinite with one to one correspondence 1 <-> -1, 2 <-> -3, 3 <-> -5, 5 <->-7......

c) The set A x Z+ where A = {2,3}

The set is countably infinite with one to one correspondence 1 <-> (2,1), 2 <-> (3,1), 3 <-> (2,2), 4 <-> (3,2)....

d) The integers that are multiple of 10

The set is countably infinite with one-to-one correspodence 1 <-> 0, 2 <-> 10, 3 <-> -10, 4 <-> 20, 5<-> -20, 6 <-> 30.......

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