overlapping

Hey, engin

I'll show the double-set matrix method below in case you want to see how that applies to this problem; I also like Stuart's solution. The below might show you conceptually why you are making the mistake you're making, though.

Given:
................in x.....not in x......total
in y............6........................18
not in y..................0
total..........10

We want to find the ones that ARE in x and ARE in y but are NOT in both. Start filling in the remainder of the matrix.

................in x.....not in x......total
in y............6...........12..........18
not in y.......4.........0..............4
total..........10..........12..........22

So look at the cells that correspond to:
in y but NOT in x: 12
in x but NOT in y: 4
Add those to get 16

What you are doing is adding the total x (10) and the total y (18) to get 28, and then subtracting out that 6 once to get 22.

If you subtract out the 6 once, you are still counting those 6 integers once in the set; you are only subtracting out the overlap. But the question asks us to remove the 6 integers ENTIRELY from the final answer, so you'd have to subtract out the 6 TWICE, which would give you 28-6-6 = 16.

You might want to try this with some real numbers - actually write out some sets of integers for x and y that fit the parameters in the matrix above so that you can see what I mean about subtracting out the 6 overlapping integers twice instead of once.