Sequencing - Mutually Exclusive Outcomes

[emslifkin]

In the Logic Games Bible 2016 edition, on pages 420 and 421, it discusses mutually exclusive outcomes. In the two examples provided, the same concept appears to be diagrammed two different ways. In the second diagram, where r comes before s and l or s and l come before r (in little triangle diagrams), I feel like this representation does not accurately represent what is being stated. If I am reading these diagrams, it appears that R comes before both other letters or after, not that r is in the middle each time. Additionally, it appears this representation is used in the explanations of any questions that involve time, weight, etc...anything besides direct order; is there a reason for this? Can you explain why the diagrams are different or are they both just valid representations of the same idea?

[Dave Killoran]

Hi E,

Thanks for the question! Those two representations show the two possible scenarios that are allowable under the phrasing of that rule. In other words, either option #1 occurs, or alternately option #2 occurs. But, one of the two will always occur (both cannot occur simultaneously since they conflict).

The key is to understand the wording of the rule:

"R sings at some time before S or at some time after L, but not both."

So, it's either:

• R S
  OR
  L R

but not both. So, let's examine what happens in each scenario:

• 1. R S
  
  When R S is in force, then the other option ( L R ) cannot occur, meaning that instead it must be R L. That means that R is ahead of both S and L, hence the triangular diagram with R on the left. In that diagram, R sings at some time before both S and L.
  
  
  2. L R
  
  When L R is in force, then the other option ( R S ) cannot occur, meaning that instead it must be S R. That means that both S and L are ahead of R, hence the triangular diagram with R on the right. In that diagram, S and L both sing at some time before R.

Please let me know if that helps. Thanks!