Asked about this the other day...Sufficient/Necessary....and when it matters

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• 6 Likes

  jknauf Alum Member

  May 2017 edited May 2017 1741 karma

  Lets take a look at question #22 Preptest 35 section 1

  This is a sufficient assumption question which reads:

  No chordates are tracheophytes, and all members of Pteropsida are tracheophytes. So no members of Pteropsida belong to the family Hominidae.

  Does the conclusion follow from our premises? No! If it did this wouldn't be a sufficient assumption!

  Mapped out, the stimulus gives us:

  C--> T/ --> P/
  .....................
  Conclusion: P --> H/

  Contrapositive:

  P-->T-->/C
  ...................
  Conclusion: H-->/P

  So what do we need to reach our conclusion and prove it to the requirement of 100% validity?

  Hmmmm, lets think back to our valid argument forms. Abstractly, the argument looks like this:

  A-->/B-->/C
  therefore
  C-->/D

  :0 oh no! I have a not C in the stimulus, and a regular C in the conclusion. What the hell? How am I supposed to match these up?

  Well, what if I take the contrapositive?

  D-->/C

  Phew! Now I have something to work with.

  So how can I reach the conclusion All D--> are not /C. Well lets think about our valid argument forms again, which are complied of sufficient / necessary conditions.

  Right now with this argument form A-->/B-->/C

  we can conclude A-->/C, but this isnt what we are looking for, we are looking for D-->/C... well lets throw that D in front of the A and see what happens..

  D-->A-->/B-->/C

  :0!!

  We can now conclude D-->/C perfectly!

  So now, lets use the real example above and plug everything back in

  H-->C--> T/ --> P/
  .....................
  Conclusion: P --> H/ (contra: H-->/P)

  Now lets apply the conditions from the stimulus to figure out exactly what our sufficient assumption must be:

  C is for chordates, H is for Hominidae

  So if all hominidae are chordates (H-->C) we can properly conclude our argument (H-->/P, or contrapositive P-->H/).

  Before even looking at the answer choices, I know this is the answer.

  Now, to answer your question

  @LSATcantwin said:
  Is there a method to identifying when mapping X -> Y on a question? What am I missing?

  No, there is no method. Sometimes, in lets say, most strongly supported questions. They will give you a huge conditional chain, and take one little tiny fact which was given to you in the contextual piece of the stimulus and make that tiny fact the one thing that supports the answer. Now you just wasted 30 seconds trying to map this thing out for nothing.

  Your understanding of when and when not to be mapping will come with time. Ultimately, the goal is to not map out conditional logic, but be able to do the mapping quickly and efficiently in your head. For sufficient assumptions, I will say, nearly every single time, mapping can be done to find the answer. A question like the one above must be done in 30-45 seconds or less if you are aiming for the high 160s or 170s. The question above has to be an automatic point, an easy bucket, or a layup if you will.

  I think what you are missing is the simple fact that conditional logic isn't always necessary to understand or arrive at the correct answer choice on all problems which conditional logic is present.

  Hell, if i sat there long enough, I could get to the correct answer for the question above without knowing my conditional logic. I could think through it piece by piece, but then this layup 30-45 second question turns into a 2-3 minute endeavor.

  It is a VERY good thing that you have worked so hard to reach an understanding of conditional logic! Now, just use it more conservatively.
• LSATcantwin Alum Member Sage ⭐

  May 2017 13286 karma

  @jknauf said:
  Lets take a look at question #22 Preptest 35 section 1

  This is a sufficient assumption question which reads;

  No chordates are tracheophytes, and all members of Pteropsida are tracheophytes. So no members of Pteropsida belong to the family Hominidae.

  Does the conclusion follow from our premises? No! If it did this wouldn't be a sufficient assumption!

  Mapped out, the stimulus gives us:

  C--> T/ --> P/
  .....................
  Conclusion: P --> H/

  Contrapositive:

  P-->T-->/C
  ...................
  Conclusion: H-->/P

  So what do we need to reach our conclusion, and prove it to the requirement of 100% validity.

  Hmmmm, lets think back to our valid argument forms. Abstractly, the argument looks like this:

  A-->/B-->/C
  therefore
  C-->/D

  :0 oh no! I have a not C in the stimulus, and a regular C in the conclusion. What the hell? How am I supposed to match these up.

  Well, what if I take the contrapositive?

  D-->/C

  Phew! Now I have something to work with.

  So how can I reach the conclusion All D--> are not /C. Well lets think about our valid argument forms. Which are complied of sufficient / necessary conditions.

  Right now with this argument form A-->/B-->/C

  we can conclude A-->/C, but this isnt what we are looking for, we are looking for D-->/C... well lets throw that D in front of the A and see what happens

  D-->A-->/B-->/C

  :0!!

  We can now conclude D-->/C perfectly!

  So now, lets use the real example above and plug everything back in

  H-->C--> T/ --> P/
  .....................
  Conclusion: P --> H/ (contra: H-->/P)

  Now lets apply the conditions from the stimulus to figure out exactly what our sufficient assumption must be:

  C is for chordates, H is for Hominidae

  So if all hominidae are chordates (H-->C) we can properly conclude our argument. Before even looking at the answer choices, I know this is the answer.

  Now, to answer your question

  @LSATcantwin said:
  Is there a method to identifying when mapping X -> Y on a question? What am I missing?

  
  No, there is no method. Sometimes, in lets say most strongly supported questions, they will give you a huge conditional chain, and take one little tiny fact which was given to you in the context and make that tiny fact the thing that supports the answer. Now you just wasted 30 seconds trying to map this thing out for nothing.

  Your understanding of when and when not to be mapping will come with time. Ultimately, the goal is to not map out conditional logic, but be able to do the mapping quickly and efficiently in your head. For sufficient assumptions, I will say, nearly every single time, mapping can be done to find the answer. A question like the one above, must be done in 30-45 seconds or less if you are aiming for the high 160s or 170s. The question above has to be an automatic point, or a layup if you will.

  I think what you are missing is the simple fact that conditional logic isn't always necessary to understand or get to the correct answer choice on all problems.

  Hell, if i sat there long enough, I could get to the correct answer for the question above without knowing my conditional logic. I could think through it piece by piece, but then this layup 30-45 second question turns into a 2-3 minute endeavor.

  It is a VERY good thing that you have worked so hard to reach an understanding of conditional logic! Now, just use it more conservatively.

  Sorry to quote the entire thing, but this may have been the single most helpful thing I've read in all my hours of studying. Thank you so much.
• 1 Like

  jknauf Alum Member

  May 2017 1741 karma

  @LSATcantwin said:
  
  Sorry to quote the entire thing, but this may have been the single most helpful thing I've read in all my hours of studying. Thank you so much.

  That's very humbling to read man.

  Thanks
• 1 Like

  Sprinkles Alum Member ⭐

  May 2017 11542 karma

  @jknauf said:

  @LSATcantwin said:
  
  Sorry to quote the entire thing, but this may have been the single most helpful thing I've read in all my hours of studying. Thank you so much.

  That's very humbling to read man.

  Thanks

  Way to go Knauf. This will come in handy for future references so I'm bookmarking.
• 2 Likes

  jknauf Alum Member

  May 2017 1741 karma

  @Sprinkles said:
  Way to go Knauf. This will come in handy for future references so I'm bookmarking.

  Well gosh! Now I need to go back and edit for grammar and punctuation. Can't have people coming back here and being reminded of my lackadaisical grammar.