Conditional Reasoning

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• 2 Likes

  Daniel.Sieradzki Member Sage ⭐

  September 2016 edited September 2016 2301 karma

  Never feel that anything is basic. This is actually kind of tricky because there is a conjunction in the conditional.
  
  This is a group 3 conditional. It can be solved by negating one of the two parts of the conditional and making that particular part the sufficient condition.
  
  Here are the two parts (this is hard because one of the parts is actually two things):
  Part 1: EW = Eye Witness & D = Defendant
  Part 2: L = Lose Case
  
  Thus, you can either negate (EW & D) and make that the sufficient condition or negate L and make that the sufficient condition.
  
  Way 1: ~L -> (EW & D)
  
  or
  
  Way 2: ~(EW & D) -> L
  
  Either way is correct.
  
  It is also worth noting that Way 2 can be also written as (~EW or ~D) -> L. This is because ~(EW & D) means not both EW and D. In other words, at least ~EW or ~D. This is known as De Morgan's Law in logic.
  
  Let me know if you have any questions. Good luck in December!
• MrSamIam Inactive ⭐

  September 2016 2086 karma

  @Daniel.Sieradzki Covered it well. One thing that I do want to mention, which Daniel implied, is that it doesn't matter which of the conditions you choose to be the sufficient or necessary - so long as you negate whichever you've chosen to be the sufficient.
• 1 Like

  MsM1998_ Alum Member

  October 2016 117 karma

  Testing my knowledge (correct me if im wrong)
  ~ L -> (EW & D) can also be split since it's an "and " in the necessary condition. In this case it would be ~L -> EW and ~L -> D, same can be done for the other version too, I think. Can someone confirm this for me? (im also trying to learn)
• M.Yanka106 Member

  October 2016 113 karma

  MrYC, you are correct about the split
• dcdcdcdcdc Alum Member

  October 2016 382 karma

  Good call on taking it a step further and splitting. Helps think about the statement:
  
  if you don't find a witness, then you lose
  if you the defendant does not take the stand, then you lose
  ---
  if you win, then you found a witness and the defendant took the stand
  
  I could see that first part of splitting the sufficient or condition as really helping solve an LR question, because it shows the minimum condition that leads to a loss.