QR2 PS 158

[nycgirl212]

I feel like the answer to this question is not worded correctly or is misleading.

The question says that there is a set but we have no information about how many numbers are in the set. all we know is that there are 2 for sure: t and t+2. By knowing that -1 is in the set, I reasoned that the -1 is either the "t" (in which case t=-1, so t+2 = 1) or that the -1 is the "t+2" (in which case t+2=-1, and t is -3). From this info we know that the set has -1, 1, and -3. nothing else. The set can be a set of 3 numbers. So why does the answer assume that -3 is incorrect and 5 is correct? We have no way of knowing if the set even goes out to 5. and Also, since the set has a -1, which could be the t+2 portion, then the set must have a -3 (as the t portion).

Sorry if that's very convoluted!

[tim]

No, -3 does not have to be in the set. Let's start with what we know: -1 is in the set. That's all. So apply the rule: If -1 is in the set, then 1 is in the set. Now apply the rule again: If 1 is in the set, then 3 is in the set. And again: If 3 is in the set, then 5 is in the set. Continuing, we see that 7, 9, and in fact every odd positive number must be in the set. The question does not have to tell us how many numbers are in the set, because the very definition of the rule REQUIRES an infinite number of elements. The key here is to pay attention to the precise wording of the rule, drawing all conclusions we can be absolutely certain of but not making any assumptions we cannot be absolutely certain of.