# Which one of the following is a complete and accurate list of architects, each of whom could be the architect assigne...

Samir on October 16, 2019

Game 2 Question 4

Can someone explain why E is the correct answer? I do not understand how G could be with Project X. If G is with Project X that means it is not with Project W therefore meaning F is with W, and if F is with W then L must be with Project Z because of the first rule. But then that causes H to be with Project Y which can't be true because H is with Project Y if F is not with Project W, but F is with Project W in this case.

Replies

Irina on October 16, 2019

@Samir-Ghani,

The game requires us to match four architects - F G H L to four projects - W X Y Z, and determine the order of the projects.

The following rules apply:

(1) Either F or L is assigned Z.

Z: F/L

(2) F is assigned W if G is not

This rule is basically saying G works on W or else F.

W: G/F

(3) H is assigned Y if F is not assigned W.

W(G) -> Y(H)
~Y(H) -> W(F)

The question asks us which of the following could be assigned to project X?

Notice that there are no rules restricting how could be assigned to X, that should be the first clue that it will be a longer list. Let's consider a scenario when G is assigned to X.

It then means that F is assigned W as you correctly pointed out,
L is assigned Z, and H is assigned Y.

W: F
X: G
Y: H
Z: L

The fact that H is with project Y is not against the rules because the proper transposition of rule (3) is IF H is not assigned Y, THEN F is assigned W. We cannot infer that H is not assigned Y just because F is assigned W, this would be a logical fallacy of affirming the consequent.

Let me know if this helps and if you have any further questions.

on October 22, 2019

Can you please set up the game board? I did not understand this answer.

Shunhe on January 8, 2020

Hi @bb427,

I'd set up the game board as a multi-linear game. We have architects who need to be matched to projects, and we need everything to be ordered.

Architects: __ __ __ __
Projects: __ __ __ __

Also note that there's only two possibilities for the architect orderings, since we know H is last and F immediately precedes G. That means the order of the architects has to be FGLH or LFGH. So we can have

F G L H
_ _ _ _

OR

L F G H
_ _ _ _

Hope this helps!

Zia on June 17, 2020

Can someone please explain the answer because if F is assigned W, it will trigger in sufficient condition for contrapositive of rule 3? Then how could X be assigned to G?