Hi @linds, thanks for your post. Notice the rule: If G is selected, K must be selected. This can be diagrammed as G ==> K. The contrapositive is: "not K ==> not G." But notice: K could be selected, without G. G is not necessary for K. K is necessary for G.
You committed an incorrect reversal in reasoning in assuming that just because K is necessary for G, G must appear if K is selected. This is false.
Moreover, notice the interaction of the various rules. First, on Question 4, you are told that F is the chairperson of the committee. F is a tenant. The second indented rule tells us that "the chairperson must be a representative belonging to the group from which exactly two representatives are selected." This means that in this case, there can only be one more tenant selected, and the other three slots will be filled by homeowners.
Who are our remaining tenants? G, J, K, and M. Well, we can't put G in, because if G is in, K has to be in too - and we only have space for one more tenant. Likewise, we cannot put in J or M, because they have to go together, and again, we only have space for one more tenant. By process of elimination, therefore, we can conclude that the second tenant slot must be filled by K.
Hope this helps. Please let us know if you have any additional questions.
KathleenDecember 14, 2021
If F is the chairperson of the committee, which one of the following is among the "people" who must also be on the committee? Since this question doesn't specify between tenants or Homeowners but rather identifies the answer as "people" and P must be selected because M is definitely out and as the rule says M or P not both how is K definitively in the answer?
jakennedyJanuary 19, 2022
Hi,
Good question! When it says M and P cannot both be selected, we would diagram it as follows:
M ? NOT P P ? NOT M
This is the same way that we would diagram “M or P is not selected”.
The here key is that, although they cannot both be selected, they can both not be selected. It seems as if you have interpreted it as:
NOT M ? P
This is similar to the original error that Mehran addressed, but applied to different letters.
Here’s how I would get to the answer:
Tenants: F G J K M Homeowners: p q r s
(I like to make one group lowercase and capitalize the other to make it easier to distinguish)
“If F is the chairperson”:
Comittee:
Tenants: F _ Homeowners: _ _ _
Not on Comittee: _ _ _ _
We know that F is in the group with only two representatives because “the chairperson must be a representative belonging to the group from which exactly two representatives are selected.
We also know that J and M are either both in or both out. Since there is not space for them to both be in, they must both be out:
Tenants: F _ Homeowners: _ _ _
Not on Comittee: J M _ _
This leaves only G and K for the final tenant. Since G ? K, we cannot put G in as there is no space for K. Thus, K must be in.
Tenants: F K Homeowners: _ _ _
Not on Comittee: J M G _
Having shown that K must be in, you can select answer choice B without ruling the rest out. There can only be one correct answer after all.
To show why they don’t work, there are four homeowners. We know F ? q, so we can put q in:
Tenants: F K Homeowners: q _ _
Not on Comittee: J M G _
Of the remaining homeowners, p, r, and s, nothing restricts them from being placed anywhere. Thus, C, D, and E are incorrect.
We already know A is incorrect because G must not be in a committee.
