LGBW Ed. 2015, Rule Origin Drill # 4, Pg. 85

[myverdict]

Rule Origin Drill Answer Key, Drill 4, LGBW, Ed. 2015, Page 85

Drill 4 question:

R > P & Q
or
P & Q > R

I am unable to diagram 4.(A) Neither P nor Q can depart earlier than R, unless they both depart earlier than R.

The answer key in the LGBW is represented as below:

P > R or Q >R --------> P & Q > R
& contrapositive as
R > P or R > Q ---------> R > P & Q

This is how I diagrammed it assuming that Neither ... nor... means "and."
P & Q > R -----------> P & Q > R

Why is P > R or Q > R represented separately and with an "or."

Please help.

[Nikki Siclunov]

Hi myverdict,

Thanks for your question. Let's look at the rule you're asking about more closely:

Neither P nor Q can depart earlier than R, unless they both depart earlier than R.

After applying the Unless Equation, the claim preceded by the word "unless" becomes the necessary condition. The remainder (neither P nor Q can depart earlier than R) must be negated to become the sufficient condition. Note that the logical opposite of "neither P nor Q" is "either P or Q", because "neither/nor" is a conjunction. Negating a conjunction requires showing that the two propositions cannot both be true.

Thus, the rule can be diagrammed as follows:

• P > R
  
  or P & Q > R
  
  Q > R

In other words, if either P or Q departs earlier than R, then both of them must depart earlier than R. By the contrapositive, if at least one of P or Q departs later than R, then both of them must depart later than R:

• R > P
  
  or R > P & Q
  
  R > Q

Since the sufficient condition of one of these rules will always be triggered, we can conclude that the relationship between P, Q, and R will always conform to one of these two scenarios:

• P & Q > R
  
  or
  
  R > P & Q

To put it another way, the only sequence that is disallowed is the sequence where R is in the middle between P and Q (regardless of the order in which P and Q depart).

Hope this clears things up!

Thanks,