Let S = {1, 2, 3, ..., 12}. How many subsets of S, excluding the empty set, have an even sum but not an even product?

Guest Jun 17, 2020

#2**0 **

I am really confused about this one, I thought the answer was 15 but that is wrong

Guest Jun 17, 2020

#3**+2 **

So

even * odd = even

odd*odd = odd

even*even.= even

even+odd = odd

even+even = even

odd + odd = even

So for subsets containing 2 we must have 2 odds.Thus all odds work.

6odds-

6c2 = 15

Trios: We must have all odds, but odd+odd+ odd = odd.so thus there are no possibilities for subsets with odd amounts.

quadruplets:

Again, odd oddd odd odd

6c4, again we have 15

6-lets

1 choice, 6c6

Thus 15+15+1 = 31

Not sure if correct, but I think it its.

hugomimihu Jun 17, 2020