I know the answer is 64 from 2^6 but I may just not be great at logic or fully know the definition of a power because I am confused on the reasoning why.
The reasoning I heard is you have 2 choices: to include an odd number or not and since you have 6 odd numbers the answer is 2^6.
I am just a bit lost on how the power represents all the subsets if there is a another way to do this perhaps with combination formulas i'd also appreciate it. (I am in Intro to Discrete)
Edit: For clarity, I mean how many subsets of A are there that contains only odd numbers. So I assume {1,3} , {1,3,5} {3,5,1} etc in that sense Also changed the title it was a typo with I mean only not all.
Best Answer
The question is really "how many subsets of $\{1,3,5,7,11,17\}$ are there, not counting the null set?"
As you said each element is either in the subset or it isn't. Thus each element has two choices, so there are $2\cdot2\cdot2\cdot2\cdot2\cdot2=2^6$ subsets, and we subtract one more since we also just counted the null set, which we don't want.
This may be easier to see with two elements, $\{a,b\}$. If $1$ represents "in the subset" and $0$ represents "not in the subset" then all possible subsets are
$0,0$, or $\emptyset$
$0,1$, or $\{b\}$
$1,0$, or $\{a\}$
$1,1$, or $\{a,b\}$