Mutually Exclusive Outcomes -- R Sings Example

[yongjook]

For mutually exclusive outcomes, example regarding "R sings at some time before S or at some time after L, but not both."

I'm am lost why the diagram looks like 1 or 2.
I feel like it should be R > S or R <L.
S
R > - - - - means that R is before S and L accrodign to Pg.371 example 5.
L

Thank you

[Nikki Siclunov]

Hi yongjook,

The rule presents two options:

R > S

or

L > R

... but rules out the possibility of both options occurring simultaneously: the options are mutually exclusive. Now, let's think about what that means:

Let's say R sings before S. In that case, it cannot be true that L sings before R. Thus, we need to ensure that L sings after R:

R > S R > L

In other words, if R sings before S, then R must sing before both S and L.

Alright, what about the second option, where R sings after L? In that case, it cannot be true that R sings before S. So, R must sing after S:

L > R S > R

In other words, if R sings after L, then R must sing after both S and L.

Taken together, these two rules suggest that there are only two possible ways to order L, R, and S: either R sings before both S and L, or else R sings after both S and L.

By the way, never ever use both ">" and "<" in creating your sequencing setups. Keep it simple and just use one of these two connectors (we prefer to use ">").

Hope this helps!

[Dave Killoran]

Earlier today, I received the following question:

Hello, I'm on page 421 of the 2016 Logic Games Bible. The diagram for the statement, "R sings at some time before S or at some time after L, but not both" doesn't make sense to me. Could this be a misprint? The way I read the diagram, the diagram would state the following: 1st diagram, R sings before S and L. 2nd diagram, S and L sing before R.

The wording of this rule is unusual, so let's take a look at it more closely. There are three notable areas, which I will show in italics below:

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

Ok, so the first two notable areas are where the rule language changes from “before” to “after.” That’s tricky, and makes a big difference! The other part is the “but not both,” which signifies that only one of the first two conditions can occur. Those two conditions control what can occur, and individually they can be represented as:

• R S
  
  or
  
  L R

When you have one of those two relationships occurring, you can’t have the other due to the “but not both.” So if we have
R S, we can’t have L R, and it must be R L instead. Combining those two leads to:

• S
  R
  L

The diagramming tools of this forum do not allow me to represent this perfectly, but the diagram is the same as the one on page 421.

On the other hand, if we have L R, then we can’t have R S, and so it must be S R. Combining those two statements yields:

• L
  R
  S

Again, the diagramming tools of this forum do not allow me to represent this perfectly but the diagram is the same as the one on page 421.

It’s a very tricky rule, and the before/after language change in combination with the “but not both” leads to a result where only these two diagrams are possible.

Please let me know if this helps. Thanks!