Answer
According to corollary 2:
$(_0^n)-(_1^n)+(_2^n)-...._-^+(_n^n) = 0$
On taking all negative terms to the RHS we get :
$(_0^n)+(_2^n)+(_4^n).... = (_1^n)+(_3^n)+(_5^n)....$
Now in the equation above the LHS represents the number of subsets with even number of elements of a set containing n elements and the RHS denotes the number of subsets having odd number of elements. The above equation shows that both of them are equal. Hence it is proved that a nonempty set has the same number of subsets with an odd number of elements as it does subsets with an even number of elements
Work Step by Step
Same as above.
