PTB.S2.G2 - a park contains at most five of seven

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• 1 Like

  BinghamtonDave Alum Member ⭐ 🍌🍌

  August 2017 8694 karma

  I took a more intuitive approach/understanding of this rule when I diagrammed it. If a more intuitive approach to this rule is not what you are looking for with your inquiry, please disregard the remainder of this post. I hope to shed some light on what I see this rule meaning in the worlds we construct for this game. In many ways, this game hinges on our ability to “see” this rule for what it is.

  “If it is not the case that the park contains both laurels and oaks then it contains firs and spruces.”

  “If it is not the case that the park contains both laurels and oaks”

  So if the park contains just laurels
  or
  if the park contains just oaks
  or
  if the park contains neither laurels nor oaks

  All 3 of those things satisfy the sufficient condition and trigger the necessary condition of
  “contains firs and spruces.” What does this mean in plain English?
  if we have just laurels and no oaks, then we better have firs and spruces
  if we have just oaks and no laurels, then we better have firs and spruces
  if we have neither oaks nor laurels then we better have firs and spruces

  All three of those instances fall under the heading of “if it is not the case that the park contains both laurels and oaks.” Those are the three possibilities that satisfy that sufficient condition. Now, what makes this so intuitively difficult for me to really get a firm grasp on? It is in my estimation the negative aspect of the sufficient condition is a bit hard to grasp. Normally we just have something like:
  “If A is in 4 then K is in 2”

  I like to read rules with a negative sufficient condition as:
  “In the absence of_______, then we have ______”
  Try it: pretend the rule is “If A is not in forth then K is in second”
  “In the absence of A in 4th then K is in 2.”
  Now, unpack that, what does “in the absence of A in 4th” mean? It means A in 5,1,2,3, and so on.

  Now what happens if we fail the sufficient condition? We know from our core lessons that the rest of the rule falls away. But what does failing the sufficient condition in this particular rule actually mean? In other words: how do we get to a failure of “If it is not the case that the park contains both laurels and oaks”? We make it the case that the park contains both laurels and oaks.

  Now that we can see what satisfying and failing the sufficient condition for this very important rule looks like, lets see what we can deduce from the necessary side of the rule: what if we fail the necessary condition? Then we must fail the sufficient condition. This poses a question: how would we fail the necessary condition of this rule?

  “…then it contains firs and spruces.”
  We could have just firs and no spruces
  or
  We could have Spruces and no firs
  or
  we could have neither firs nor spruces
  All three of these options we would fail the necessary condition of “firs and spruces”

  For each of those options we know that we cannot have a fulfillment of the sufficient condition: namely for each of those options we cannot have:
  if we have just laurels and no oaks…
  if we have just oaks and no laurels…
  if we have neither oaks nor laurels…

  So what must we have when we fail the necessary condition of this rule? We must have a failure of the sufficient condition, namely:
  the park contains both laurels and oaks.

  Lets again take a look at how we have broken down the rule so far:

  if we have just laurels and no oaks, then we better have firs and spruces
  if we have just oaks and no laurels, then we better have firs and spruces
  if we have neither oaks nor laurels then we better have firs and spruces

  Now look what happens when we fail the necessary condition:
  if we have just firs and no spruces then we better have both laurels and oaks
  if we have have Spruces and no firs then we better have both laurels and oaks
  if we have have neither firs nor spruces then we better have both laurels and oaks

  In summation, what use is all of this? Is it overkill? Maybe, but lets take a quick look at question 10. A deeper understanding of this rule puts us in a position to answer question 10 much easier than we would otherwise in my estimation. The absence of Firs in the park triggers a whole series of events that if followed carefully forces us to choose Y which in turn forces M outside of the park. Sometimes on question the LSAT writers will "stop" at a certain point and the MBT answer chocie will be 1 step away. Here it was 3 or 4 steps away, but it is a rewarding point to get on such a tough section. Very difficult question made several levels simpler by our understanding of the rules garnered through practice.

  I hope the above help, more specifically, I hope it helps in a different/more intuitive way than a mere translation of the rule.

  David
• MsM1998_ Alum Member

  August 2017 edited August 2017 117 karma

  Thank you @BinghamtonDave , very good and detailed response to help understand the rule in an intuitive way. I thought of it in this way as well when doing the question, but it ended up colliding with my previous knowledge about how to contrapose these statements. In this case, can we not get the same practical understanding through using our lawgic rules for AND/OR statements? I ended up getting stuck for this reason, since much of our ability to solve LG is based on conditionals and lawgic...If we can't get this right through strictly lawgic, then its kind of an eye-opener for me.. Will have to remind myself not to solely rely on lawgic
• 1 Like

  nathanieljschwartz Alum Member

  August 2017 1723 karma

  FANTASTIC explanation @BinghamtonDave !! Spoken like a true afficianado !
  ( lol good thing we arent tested in spelling, i butchered that so bad, my spellcheck couldnt even help)