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Hello,
I am unclear about the diagramming for this question below:
PT37.S2.Q12
Admin Note: I deleted the question as it is against our Forum Rules to post LSAT questions verbatim.
JY's diagram is below, but I am not sure why "without" did not warrant the negation of the sufficient (GS) and "cannot" the negation of the necessary (/GF) so that the diagram is /GS-->/GF. How do I get to the bolded translation below?
GM-->/BF
GF-->/BS
GS-->GFm-->CV
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6 comments
Great! Thank you very much to both! I can see the connection now.
@dimakyure869 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 :)
You cannot have GS without GFarm.
If you have GS you have GFarm
or
If GS then GFarm
or
GS→GFarm
@dimakyure869 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
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?
Thank you!
The 'cannot' applies to all 4 parts of the entire phrase sentence, so it translates into:
(cannot) GM from BF = GM → GFood (/BF = GFood)
(cannot) GFood from BS = GFood → GS (/BS = GS); 1 & 2 chain into GM → GFood → GS
(cannot) GS without GFarm = GS → GFarm
(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 !! :blush: Hope this helps for your diagram.