Self-paced
Curious how everyone would do this. Try telling me before reading all this, or even just skip reading what I did, I really am curious purely what shorthand everyone uses for conversions.
Ok I just started learning about lawgic and came back to this question. I need some help.
I'm convinced mapping to lowgic is the fastest way to do this in the long run. But currently, I'm really slow at it. I just spend 5:30 on this question!
My problem is reading and mapping to the same thing deterministically. For this question I accidentally mapped like this:
Turned "price it pays for coffee beans continues to increase" into "GC" for "Greater Cost", and "the Coffee Shoppe will have to increase its prices" into "GP" for "Greater Price". So, GC -> GP. So far so good.
Then "either the Coffee Shoppe will begin selling noncoffee products or its coffee sales will decrease" into "NC | DS" for "Non Coffee OR Decreased Sale". So now I have GP -> NC | DS.
Then I turned "decrease the Coffee Shoppe's overall profitability" into "DP" for "Decreased Profitability". So now NC -> DP
Then I turned "can avoid a decrease in overall profitability" into "/DOP" for "NOT Decreased Overall Profitability" and "coffee sales do not decrease" into "/DCS" for "NOT Decreased Coffee Sales". Notice this is where I messed up. I mapped things I had already defined into new acronyms. I had:
GC -> GP
GP -> NC | DS
NC -> DP
/DOP -> /DCS
But I should have had:
GC -> GP
GP -> NC | DS
NC -> DP
/DP -> /DS
Now its obvious that
DS -> DP, and since also NC -> DP, then now NC | DS can just be set to DP, giving:
GC -> GP
GP -> DP
Therefore GC -> DP, and back to english is "If cost of beans increase, Shoppe will have decreased profits", which is exactly what C says, so it took me 3 seconds to find that. But getting to GC -> DP was the key.
...So how do I make that faster, and how do I avoid mistakes like mapping the same thing to two different lawgic acronyms? That is what took all my time to realize I had done that, which is why nothing was coming out of the original mappings I had. Maybe there is better shorthand to use that would help me be more clear, but also short enough to be fast still?
I will try again now after writing all this:
Mapping First:
Bean price increases -> Shoppe increases prices
Shoppe increases prices -> Sells NCP | CSD
Sells NCP -> DOP
/DOP -> /CSD
------------------------
Now Transformation:
CSD -> DOP
Sells NCP | CSD -> DOP
Shoppe increases prices -> DOP
Bean price increases -> DOP
"If bean prices increase, then Coffee Shoppe will have a Decrease in Overall Profitibility", answer C.
...Ok that was a bit faster, but typing was slow, probably faster on paper. Still trying to find that balance of clarity and brevity. If a person could just instantly map this all to something like
BPI -> SIP
SIP -> NCP | CSD
NCP -> DOP
/DOP -> /CSD
-------------------------
CSD -> DOP
NCP | CSD -> DOP
-------------------------
BPI -> SIP -> DOP
BPI -> DOP
-------------------------
"if Bean Price Increases, then Decrease in Overall Profitability", answer C.
That would be soooo fast. That is my goal. Acronyms are so much faster to read and move around in lawgic, but how important is retaining the context of each in your voice in your head? Curious what everyone would do and if you actually read everything I did, thank you and I would love to hear what I can do to improve so I can do this without even thinking.
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5 comments
It may be that mapping this out is a useful tool for developing your understanding, but it is very likely not the fastest way of answering this question.
When I read it, I thought, "Alright, if prices go up, a chain of events will lead to A (Non-coffee products) or B (Lower sales). Both A and B mean profits will decrease.
What do I know from this? If prices go up, decreased profits are unavoidable."
C). Done. You don't need a quick acronym trick, you just need to notice it is setting up a situation in which decreased profits are inevitable. We are given two roads (A or B, non-coffee products or decreased sales) and both lead to decreased profits.
The question is written in a way to get you lost in the weeds, but the structure is very simple. The one tricky bit may be translating the last sentence into words you understand. "The coffee shop can avoid decreased profitability only if its sales do not drop" just means, "If sales drop, decreased profitability." Combine that with, "If non-coffee products sold, decreased profitability" then we know profitability must decrease if bean prices/coffee prices go up. We were told if that happens, those are the only two options.
@Karl! Yeah this is much faster and I am mainly interested in just being faster. You are right that the tricky bit for me is that last sentence. It makes me go "whoa let me diagram this", but I think in reality I just need to think "is there a simplified way of phrasing this", ie "if sales drop, profits drop", which unlocks the whole A -> B | C, and both B & C -> D so A -> D much easier without explicitly diagramming it.
Thank you for the insight!
@danjpeach96 welcome! I think the last sentence is the hard one. I read it and also thought, “ok wtf does that mean.”
I thought something like, “well, the only universe in which profits don’t drop is one where they don’t lose sales. The only way for that to happen is for them to sell non/coffee stuff, but that’s decreased profits too. Well, looks like they’re going to have decreased profits if these prices go up.”
It was only in hindsight that I simplified it all to, “if X happens, A or B. Both A and B lead to decreased profits.” That also simplifies out the beginning chain of bean prices up > coffee prices up and replaces that relationship with X to make it easier.
I did read through the lawgic that you have diagram and I think it would be faster if you could combine some of them! Eventually, diagraming the conditionals would come to you naturally and would not have too much trouble doing them.
Following is how I mapped:
Price CB ↑ → CS ↑→ Sell non-coffee product OR Sale ↓ → Overall profitability ↓
Avoid Overall profitability↓ → /CS↓
Going through the answer choices, C would be the only one that will work out!
I think one way you can improve is keeping in mind all the words that indicate sufficient and necessary conditions, and identify exactly where the arrows should point toward. Also, if there are things you can combine, try combining them (For example, if a premise says A→B, B→C, then directly diagraming them as A→B→C)
I used to frequently refer back to my notes when doing diagramming but now it comes naturally to me.
Took me a bit but figured out how to type ↑ ↓ ← →, so thanks for that.
I like the "immediately compress as you go"
Given:
BP↑ → SP↑ -> NCP or CS↓
NCP → OP↓
/OP↓ → /CS↓
-------------------
Then:
CS↓ → OP↓, so NCP or CS↓ == OP↓
BP↑ → SP↑ → OP↓
BP↑ → OP↓: Answer C
I'll get faster. This helped, TY