Group Games Questions - - Question 19

Which one of the following could be a complete and accurate list of the doctors that are at Souderton?

shafieiava October 11, 2019

Game set up

I understand why you deduce that in rules number one and two not both doesn't apply in this particular case. However I'm having trouble distinguishing that language from not both. It would be immensely helpful to see the same two rules written out in a way that would make a not both rule apply. Thank you!

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shafieiava October 11, 2019

A second part of this question is how the instruction makes the deduction by comparing the necessary conditions. Can someone explain why you would know for example, that the not both rule doesn't apply in rule 4 because the necessary condition of that rule has O in group R and N in group S? Thanks in advance for your time.

Irina October 11, 2019

@shafieiava,

If I understand the question correctly, you can tell by the way the rule is phrased that it does not preclude both.

(1) K is at R if J is at S

This is a conditional rule that tells us that if J is at S, then K has to be at R. The transposition of this rule is that If K is not at R, we know that J is not in S. Do we know anything about the case when J is not in S? Not really, it is plausible that J could be in R, and K also could be in R, or J could be in R and K could be in S, there are no rules that dictate the placement of K when J is not in S.

To exclude the possibility of both J and K being in R together, the rule would have to say - "If J is not in S, then K is." Then we could infer that:
~J -> K
~K-> J

Meaning one of them always has to be in S, and both could not be in R.

(2) If J is at R, O is at S.

This rule similarly only tells us the placement of O if J is at R, we cannot tell anything about the placement of O if J is at S, thus both of them could be at S. To exclude the possibility of both, this rule needs to be phrased as "If J is not at R, then O is"
~J -> O
~O -> J