Why Half of Subsets Have Odd Number of Elements – Discrete Mathematics

Question

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.

Answer 1

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