Q17

[mcmassier]

Can someone show me the quickest way to arrive at this particular answer...I believe I'm missing a key inference as opposed to trying each option. Thanks!

[ohthatpatrick]

Hey, there.

If you had initially set up two frames, this question would go a lot more smoothly.

We know initially that we're taking 7 people: F, G, H, I, W, X, Y and assigning them into three different groups.

Furthermore, we know the quantity in each group.

M: __
P: __ __ __
S: __ __ __

(normally, we'd represent these vertically, but that's hard to illustrate within the typing limitations of this text field)

The first rule gives us a chunk: HY

Just as in ordering games, chunks are often the key to inferences or the basis behind making frames in grouping games.

What are the options for the HY chunk? It can't go in Management, since that's a one person group, so it has to go in either Production or Sales. Here's where we might choose to draw 2 frames.

Frame 1
M: __
P: H Y __
S: __ __ __

Frame 2
M: __
P: __ __ __
S: H Y __

From rule 4, we know that F is always in Production, so our frames would really look like this:

Frame 1
M: __
P: H Y F
S: __ __ __

Frame 2
M: __
P: F __ __
S: H Y __

The other two rules are that F and G are enemies (can't be in the same group) and the conditional
Xs --> Wp
~Wp --> ~Xs

The fact that F and G can't be together doesn't tell me anything in Frame 1, since F's group is already full. So we already know that G will be in a different group.

In frame 2, it means that G can't be in Production. So we could add that to Frame 2:

Frame 2
M: __
P: F __ __ (~G)
S: H Y __

Does the conditional rule tell me anything for either frame? Well, I don't see X in Sales in either frame. However, the contrapositive definitely applies to Frame 1. I can see that W will NOT be in Production, therefore X can NOT be in Sales.

If X can't be in Sales, it must be in Management. We can adjust frame 1:

Frame 1
M: X
P: H Y F
S: __ __ __

Of course, now that the other 2 groups are full, everyone else has to go into Sales:

Frame 1
M: X
P: H Y F
S: G W I

If you're not currently writing the contrapositive any time you write a conditional rule, hopefully this illustrates to you that you might be missing out on seeing valuable inferences by failing to do so.

So our two frames end up looking like this:

Frame 1
M: X
P: H Y F
S: G W I

Frame 2
M: __
P: F __ __ (~G)
S: H Y __

To answer Q17, I would just look at the Sales column in each of my frames:
A) CBT, in frame 1
B) MBF! GX isn't going to happen in frame 1, since frame 1 already has a full Sales group (GWI) .. and GX can't happen in frame 2, since we already have HY in Sales (there's only room for one other letter)
C) CBT, in frame 2
D) CBT, in frame 2
E) CBT, in frame 2

CBT = could be true, MBF = must be false

Hopefully this makes sense. Let me know if you have any questions.