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Suppose that a set has an odd number of elements. Explain why half of the subsets will have an odd number of elements .

Now assuming set A is the set with an odd number of integer elements{1,2,3,4,5}

Subset b ={1,2}

subset c={3}

Subset d={4,5}

Now there are two subsets with even number of elements and one subset with an odd number of elements.It seems to contradict the earlier theorem that i have to prove.I think that i am missing something.

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    I think the downvoting here is rather hash. Is it just because the OP lacks understanding of hist own question? That's what asking is for! The question itself is perfectly good: It is plain and clear what the question is, and the OP shows enough work of his that we can see what the problem is. More questions should be like this!2012-12-30

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Hint: try pairing each subset with its complement ...

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    @HenningMakholm Brain drift - it must be Christmas2012-12-30