Group Games Questions - - Question 19

The committee must include at least one representative from which one of the following pairs?

jbenav246@gmail.com January 12, 2021

Why not M/P?

I understand that the instructor got the answer C from looking at the previous hypothetical, but in the pervious hypothetical I further placed P 'in' due to the 6th rule saying M and P cannot be together. Based off this rule, wouldn't D be the right answer, because if they cannot be together, as in not both, then wouldn't at least one variable be out, and the other in?

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shunhe January 13, 2021

Hi @jbenav246@gmail.com,

Thanks for the question! Well, let’s say we keep M and P out. So remember, the rule relating M and P says that both cannot be selected. But that doesn’t mean that one has to be selected. They could both be not selected. Basically, we diagram that rule

M —> ~P
P —> ~M

So ~M and ~P doesn’t trigger either of these conditionals here.

With M and P out, we also have to kick out J because of the second to last rule. So J, M, and P are out. That leaves F, G, K, Q, R, and S. We need to pick 5 out of 6 of these people to be in. And there are a number of ways to do that that will satisfy the rules. Consider, for example, FGK from the tenants, and QR from the homeowners. Since we can have both M and P out, it’s not the correct answer.

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

Dredd December 26, 2021

I had a game board with Jm, RSQ which doesn't violate the rules but seems to suggest an example contrary to the correct answer.

Dredd December 26, 2021

never mind I re read the question

Ravi February 12, 2022

Happy to see you got things squared away!