PT37.S2.Q12 - Rosen's statement

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• 1 Like

  hopefulling Member

  December 2020 edited December 2020 905 karma

  The 'cannot' applies to all 4 parts of the entire phrase sentence, so it translates into:

  1) (cannot) GM from BF = GM → GFood (/BF = GFood)
  2) (cannot) GFood from BS = GFood → GS (/BS = GS); 1 & 2 chain into GM → GFood → GS
  3) (cannot) GS without GFarm = GS → GFarm
  4) (cannot) GFarm without CtPV = GFarm → CtPV; 3 & 4 chain into GS → GFarm → CtPV

  all 4 chain into GM → GFood → GS → GFarm → CtPV

  !! Realized that GF was standing in for both good food and farming, yikes !! Hope this helps for your diagram.
• Bagelinthemorning-2-1-1 Core Member

  January 2021 476 karma

  Thank you!
• Bagelinthemorning-2-1-1 Core Member

  January 2021 476 karma

  Just to clarify, when we apply cannot, we negate the NA and when we apply without, we negate the SA. With these two rules, wouldn't the third logic be

  (cannot) GS without GFarm = /GS → /GFarm

  How did JY cancel out the negations?
• 1 Like

  canihazJD Alum Member Sage ⭐

  January 2021 edited January 2021 8491 karma

  You cannot have GS without GFarm.

  If you have GS you have GFarm

  or

  If GS then GFarm

  or

  GS→GFarm

  @Bagelinthemorning said:
  (cannot) GS without GFarm = /GS → /GFarm

  This is backwards. Considering this statement in isolation, GS is your sufficient condition. So if you don't have GS you can infer nothing. If you go this route, use the "without" as "if not".

  So, if not GFarm you cannot have GS

  or

  /GFarm→/GS
• 1 Like

  hopefulling Member

  January 2021 edited January 2021 905 karma

  @Bagelinthemorning I like to think of this combo (cannot ... unless // group 4 ... group 3) as double negatives that cancel each other out in the final translation. (But, this doesn't work in reverse with 'group 3 ... group 4' as neatly, you would have to also flip A → B into B → A ... but I don't want to be off-topic/confusing). But, it makes for an almost instant translation tip.

  • whenever I see this: you cannot do A without B. I automatically see:
    cannot A → without B. A → B.
  • whenever I see this: without A you cannot B, I automatically see:
    cannot B → without A; B → A.

  With Group 3 (the without), you negate the sufficient term: A → B becomes /A → B. With Group 4 (the cannot), you negate the necessary term: A → B becomes A → /B. So you're correct in your thinking, but with the example there's the need for a '2-step' process: In a way you just missed the step of flipping the terms through the translation process, but you also need to negate both (which happens in the 2-step translation).

  • (cannot) GS without GFarm = /GS → /GFarm - - you actually end up with a mistaken reversal
  In the process of working both indicators the negatives end up cancelling out.

  • Step-by-step process: the original statement,

  • STEP 01: Group 3,
    /GFarm → GS

  • STEP 02: Group 4,
    /GFarm → /GS ; contrapositive = GS → GFarm.

  • CONSOLIDATED: because of the nature of 'cannot' being equiv to 'not' /, if you start by translating the cannot into a regular 'not,' you combine the steps:
    /GS without GFarm = GS → GFarm.

  Hope that helps to clarify
• Bagelinthemorning-2-1-1 Core Member

  January 2021 476 karma

  Great! Thank you very much to both! I can see the connection now.