How to solve this question? Forum

[Woopdeedoo]

Hey guys, i'm studying the logical games powerscore bible right now, and I'm stuck on a question. It's page 117.

"A university library budget committee must reduce exactly five of eight areas of expenditure --G, L, M, N, P, R, S, and W -- in accordance with the following conditions:
If both G and S are reduced, W is also reduced
If N is reduced, neither R nor S is reduced
If P is reduced, L is not reduced
Of the three areas L, M, and R, exactly two are reduced"

1. Is this the correct way to diagram/go about solving this problem?
GrSr --> Wr
Nr --> ¬Sr
Pr --> ¬Lr
2 of LMR

_ _ _ _ _ _ _ _
R R R R R ¬R ¬R ¬R

pos 1 - L R _ _ _ M _ _
pos 2 - L M _ _ _ R _ _
pos 3 - M R _ _ _ L _ _

2. I don't understand the answer, in the book it says
"2. Because three of the group of G, P, W, N/S must be reduced, this means that...
If G is not reduced, then P, W, and N/S must be reduced.
If P is not reduced, then G, W, and N/S must be reduced
If W is not reduced, then G, P, and N/S must be reduced."

I understand that 3 of of those letters must be reduced, but how do they know that 2 of GPW are always being reduced?

[PoliticalJunkie]

Almost there bud.

1. Rules look good, just remember to write down the contrapositive of all of them (you missed some big deductions not doing this)

The scenarios are

1. IN: LM_ _ _ OUT: PR _
2. IN: LRGSW OUT: PMN
3. IN: MR _ _ _ OUT: NL _

In 2, you have R already in the IN group. Take the contra of rule 2 and you get if R then NOT N meaning N is out and GSW are in the in group.

Before anything, you only have 3 open spots in each of the groups. The remaining variables are (1) GSWN and (3) GSWP.

Because there are 3 spots remaining you know 3 of GSW P/N must be reduced. You can then run through two options (1) run through more scenarios or (2) diagram out rules pertaining to the the above.

You know that 2 of GPW are reduced because of the N/S rule. Take scenarios 1: IN LMGSN OUT: PRW (violates rule 2)

[Woopdeedoo]

ahhh, ok that makes sense!! thanks buddy

[was437]

Almost there bud.

1. Rules look good, just remember to write down the contrapositive of all of them (you missed some big deductions not doing this)

The scenarios are

1. IN: LM_ _ _ OUT: PR _
2. IN: LRGSW OUT: PMN
3. IN: MR _ _ _ OUT: NL _

In 2, you have R already in the IN group. Take the contra of rule 2 and you get if R then NOT N meaning N is out and GSW are in the in group.

Before anything, you only have 3 open spots in each of the groups. The remaining variables are (1) GSWN and (3) GSWP.

Because there are 3 spots remaining you know 3 of GSW P/N must be reduced. You can then run through two options (1) run through more scenarios or (2) diagram out rules pertaining to the the above.

You know that 2 of GPW are reduced because of the N/S rule. Take scenarios 1: IN LMGSN OUT: PRW (violates rule 2)

I've really got to stop doing LG when I'm not in a sober state! I have been sitting here trying to figure out how the hell you came up with 3 of GSW P/N must be reduced...or more specifically...how you know it was either P or N...and why...they are already solved...and how the next guy totally got it...no more smoke for me! lol.

Wouldn't W always have to be reduced?