LG Problem Set 2: Game #14

[moshei24]

Hi! Good Morning (or night or afternoon)!

The last rule in the game was "F must be played immediately after R, unless G is played earlier than R." I found that rule difficult to decipher. In the end I deciphered it as follows:

R>G --> [RF] with the contrapositive being *not* [RF] --> G>R

Did I set it up correctly? Also, is there a quick way to decipher that kind of langugage?

My complete game setup (didn't realize two of the inferences until the middle of the game) was:

H>V; V_S or S_V; [FS] or [SF]; *not* [DD]; *not* [BB] (realized this one on question #20); the rule above; the not laws were that V and S can't be first (I realize S not law on question #23) and H can't be last. Also the order by type is DBDBDBD. R/X is first.

Was I missing any inferences?

Thank you!

[Nikki Siclunov]

Your set-up is correct, and so are your inferences. Indeed, the rule that drives this game is the alternating sequence of Ballads and Dances, which you could add as a second variable set stacked on top of the first (e.g. conceptualize this as an Advanced Linear Game with two stacks: B/D and song names). You should have closely examined the 1st and 7th position in order to determine any applicable not-laws (S and V cannot be first).

As far as the conditional "unless" rule, approach it as you would any other "unless" statement: the clause modified by the word "unless" is the necessary condition. The remainder must be negated to become sufficient. Thus:

NOT [RF] --> G > R

The contrapositive is likely to prove helpful. Since the game does not allow multiple songs to be played at the same time, the logical opposite of G > R is R > G:

R > G --> [RF]

Hope this helps!

[moshei24]

Oh, so I just derived that conditional statement as the contrapositive instead of how it should have been.

Thanks!