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The first clue in this game says "G moves the sofa if, but only if, H helps move the Recliner". I missed two questions because I couldn't pick between two answers because I missed the logic in this. I looked up the explanation and I see that it has the logic written as:

GS --> HR; ~HR --> ~GS

HR --> GS; ~GS --> ~HR

But I can't but my mind around how to conceptualize this so I can find it on my own.

Youre making it way more complicated than it needs to be.

If G is in there and moves the sofa, then you know that H moved the recliner.

If H did not move the recliner, then you know that G cannot move the sofa.

This game wasnt difficult. Plot out the possibilities and you'll be fine.

Good luck!

Yeah I wrote the logic as you did, but the only two I missed on this section was this game. When I looked up the explanation as of why, it had the logic written as I did above. I was wondering if someone could explain how the "if and only if" leads to the "HR --> GS; ~GS --> ~HR" part.

Im sorry I dont have this game in front of me, but that HR to GS stuff seems like its the mistaken reversal. Are you sure thats what the game was asking for?

H moving the recliner doesnt mean that G will always move the sofa. You can have H moving the recliner and G moving something other than the sofa.

No, Im not sure, but this is what the Princeton Review explanations say so thats why Im asking, I don't understand. It seems like it would be true because I couldn't figure out the two questions that I missed on this game because it seemed like something was missing. The "if and only if" part is what gets me, I don't understand how to write the logic.

Im sorry. I guess I cant help you. I dont have the game in front of me, but I know I did very well on that game. Im not going to argue with Princeton review, but it seems like funny logic. I diagrammed the rules, the contrapositives and then the possibilities.

Lets see if anyone else can help.

The if and only if always creates a double arrow and a double not arrow.

GS<---->HR

GS<--/-->HR

The contrapositives of GS--->HR and HR---->GS give you all 4 rules (GS--->HR, xHR--->xGS, HR---->GS, xGS---->xHR)

G moves the sofa if, but only if, H helps move the Recliner.

You have to be aware of the "if, but only if."

If H moves the R, G moves the S. HR-->GS

Then using the "only if" to introduce the necessary

Only if H moves the R, G moves the S. GS-->HR