2. We will call a set of distinct natural numbers from 1 to 9 good if the sum of all numbers in it is even. How many good sets are there?
2. Answer: $2^{8}=2^{9} / 2$.

There are $2^{9}$ sets in total, and we will show that exactly half of them are good. Indeed: since the sum of all numbers from 1 to 9 is odd, the complement of a good set is bad and vice versa.