The problem involves determining all possible subsets of even numbers from the set {1, 2, ..., n}, where n is specified to be an even number. The inclusion of the empty set as a valid subset is also noted.
The discussion includes attempts to clarify the original question and the reasoning behind the calculations. Some participants express uncertainty about the correctness of the reasoning and seek confirmation. Guidance is provided regarding the inclusion of the empty set in the total count of subsets.
Participants are navigating the distinction between counting all subsets versus non-empty subsets, with specific emphasis on the requirement to include the empty set as a valid subset in this context.
You should add a few sentences to explain your reasoning. And the question is "what are", not "how many", so can you say something more about them?.agargento said:I think the answer is 2n/2 ... to include just even numbers. Is my reasoning correct?
FactChecker said:You should add a few sentences to explain your reasoning. And the question is "what are", not "how many", so can you say something more about them?.
That is better. It never hurts to add a brief explanation like that.agargento said:Just bad translation on my part. "How many" is more correct. As for reasoning, we were taught in class that for n objects, you have 2n possibilities for subsets. So I thought that because we have n/2 objects (we want only even numbers) 2n/2 is the answer.
FactChecker said:That is better. It never hurts to add a brief explanation like that.
It is correct. The odd numbers are irrelevant.agargento said:But is it correct?
PeroK said:It is correct. The odd numbers are irrelevant.
Oh now I got it. Thanks!PeroK said:That's the empty set. That is included as one of the ##2^n## subsets. If you are looking for non-empty subsets then there are only ##2^n -1## of those.
In this case you were explicitly told to count the empty set.