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asked in Set Theory & Algebra by Boss (6.5k points)   | 54 views

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Answer (A) and (B).

Subset of a countable set is countable. Set of all integers is countable and hence any subset of it is also countable.

Power set of a finite set is finite and hence countable.
answered by Boss (6.8k points)  
Thank you
I doubt about A. How do you map the subset to a number line of integers?
Enumeration method:

Go in incresing order of absolute value. In a particular absolute value, go in increasing order of the value.

Start from |0| ->0.

Then |1| -> -1,1

Then |2| -> -2,2 and so on.
@GateSet

I think you meant

-1,1 -> |1|

-2,2 -> |2|

right?
Exactly
Thanks. Can you give me any good reference where the any ideas about how mappings are done is given?
As such I have no reference which I can give. I will try to find if there is any. Anyways, you an solve these type of questions intuitively.
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