So I have a problem which defines two sets: $A = \{1,3,5\}$ and $B = \{ 1,2,3,4\}$. The question asks for the number of subsets of $A \cup B$ that contain an odd number of elements. I know the answer is $2^{5-1} = 2^4$ but I do not know why. I asked a professor what if the question asked for even numbers and he said it would be the same. I know that the number of power sets is $2^n$ where $n$ represents the number of elements in the set. I even tried writing out each subset in the power set.