# Given the following survey results, how many people like C only?

##
- 21 people like Product A
- 14 people like Products A and B
- 12 people like Products A and C
- 8 people like Products A, B and C
- 26 people like Product B
- 14 people like Products B and C
- 39 people like Product C

- 21 people like Product A
- 14 people like Products A and B
- 12 people like Products A and C
- 8 people like Products A, B and C
- 26 people like Product B
- 14 people like Products B and C
- 39 people like Product C

21

For each product, there will be people who like it only (ex. A only), people who like it and one other (ex. A and B only) and those who like all three. Let's work through this.

I'll note that this question appears to be a more fleshed-out version of this one posted earlier in the week: https://tutor.hix.ai where the total number of likes for C was 39. I'll use that figure in here.

For product A, 21 people in total like it. 14 people like A and B (and might like C), 12 like C and A (and might like B), and 8 like A, B and C. This means that we need to subtract the 8 (those who like all three) from the numbers listed for people liking two products. This will give us:

For Product B, 26 people like it. 14 like A and B (and might like C), 14 people like B and C (and might like A), and 8 like all three. We can do the same sort of math for this that we did for A:

We can now do C. 39 people like C. 4 people like C and A only. 6 people like B and C only. And 8 like A, B, and C. Therefore:

I want to note that when I first started working with A that if we take the numbers given as "only", we'd end up with something that made no sense:

A total likes = 21

A, B likes = 14 A, C likes = 12

which puts us at 26 likes, which is more than the 21 given. And so I realized we needed to subtract out from the A, B likes, for instance, those people who also liked C.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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