Which one of the following pairs of employees is such that at least one member of the pair volunteers?

Maria-Marin on April 17, 2020


I have several questions about this game. 1. Why in/out I really can't get how to determine that this was an in/out game. When I did it, I did consider the option but dismiss it because the "passage" just mentions that some out of the 7 parents will be volunteers, so it gives 7 spaces that could be filled, but it NEVER tell us something about having 7 parents and just X (< 7 )number of spots 2. How and why we should think that when a rule that (if not X -> Y) is an "either or" rule and no a "not both"? 3. Why D is wrong in this specific question (12) I'd really appreciate the help!! thx

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shunhe on April 17, 2020

Hi @Maria-Marin,

Thanks for the question! Let me answer your questions one by one.

1. We know it’s an in-out game because we know that there are two groups of people: volunteers, and not volunteers. The parents can either be in one group or the other, and there are rules about the parents that say that when one is “in,” another is “out,” and things like this. All of these indicate that it’s a in/out game.
2. So the rule “if not X, then Y” is always going to be an “either or” rule, and not a “not both” rule. Because take a look at what it’s saying. If X is not picked, then Y is picked. Now take a look at the contrapositive, “if not Y, then X.” In other words, if Y is not picked, then X is picked. This is why it’s an “either/or” rule, because one of them is going to be picked. But here’s the thing: let’s say Y is picked. Well, the original condition and its contrapositive only tell us about situations in which one isn’t picked, which means that if Y is picked, it’s consistent with X being picked or not being picked. And vice versa, if X is picked, Y could be picked or not picked. The only situation that can’t happen is that both aren’t picked, but it’s certainly possible that both can’t be picked.
3. (D) is wrong in this question because we know that neither R nor S have to volunteer. Let’s say neither of them volunteer; then we can have V and L volunteer based on rules 3 and 4. And then the other volunteers can be filled in in a number of ways. Indeed, one possible group would just be V and L, with everyone else out, as that doesn’t violate any rules.

Hope this helps. Feel free to ask any further questions that you might have.