Answer
512 subsets with odd number of elements.
Work Step by Step
If the set has 10 elements , then the number of subsets with $k$-elements is given by $C$(10,$k$)
In our case we take $k$ = 1,3,5,7,9
Number of subsets = $C$(10,1)+$C$(10,3)+$C$(10,5)+$C$(10,7)+$C$(10,9) = 20 + 120 + 252 + 120 + 20 = 512
