Are these lawgic translations correct?

Keyboard123

1

A cannot B without C.
Translation:
AB --> C
/C --> /AB

2

A without B cannot C.
Translation:
/AB --> /C
C --> AB

I'm curious about the logic itself because if it's true then it's a great thing for me to memorize so I can quickly translate group3/group 4 indicators when they appear together on the test.

castrone

im honestly super confused about how you're representing and writing the phrases
is this what u mean by: a cannot b without c
Molly can't jump if she doesn't have shoes
if Molly jumps then she has shoes

bc if it is you don't need three things just make Jump "A" and shoes "B"

if A then B
if /B then /a

Keyboard123

@castrone Thanks for replying. No I didn't mean it like that. I should have supplied examples. Here are the type of statements that inspired this post (in the stimulus and answer choices). I'm trying to generalize a way to translate "....cannot...without..." and "...without...cannot..." statements.
https://7sage.com/lesson/beijing-lhasa-pm-question/?ss_completed_lesson=1132
"Beijing Lhasa - PM Question"

phosita_phoeatah

Apologies if this strays OT a bit, but b/c of the way I was first introduced to logics, I have a tendency to "over-write". For the question posted immediate above (involving cities B, L, C, and X), I initially mapped it as follows.

1) BL --> BCL (an intermediate stop is implied by antecedent of 1)
2) BC --> BXC (another intermediate stop is implied by antecedent of 2, which itself is part of the consequent of 1)

I personally think that writing each premise as above (as opposed to BL --> C) is better, as it better represents the relationship among the three cities. Writing BL --> C does not necessarily connote how B, C, and L are related (or it might in your head, but that takes up brain space).

In terms of the question itself, as directionality of each relationship is immaterial (as in it never forces you to consider situation such as L to B ), I "got away" with representing the scenario this way. The larger point of the question is the premise "buried" within part of the consequent of the first premise.

And for this particular question (and the answer choices being considered), the directionality turned out to be immaterial (and is possibly a red herring), but this may not be the case for other questions where the same fact pattern is introduced.

As for the OT part, I wonder if I should have used a special symbol (e.g. "-->>" or "==>") to better represent the directionality aspect, as a regular arrow looks like the one used for conditional statements. Or perhaps it's better not to use special symbols that may be more descriptive, as they would require more time and may end up being immaterial for a particular question?

castrone

@Keyboard123
"an air travler in Beijing cannot fly to Lhasa without first flying to chengdu"
would translate to: If fly to Lhasa then flew to chengdu first, if a then b

castrone

@Keyboard123 I don't think you should think about "air traveler" as "a" as I suspect you are.

Keyboard123

@castrone I see why you might say that, but my translation did come out to what you said would be the correct translation.
If we apply my translation rule:
A = an air traveler in Beijing
B = fly to Lhasu
C = first flying to chengdu

"A cannot B without C"
Rule: AB --> C
If (AB) an air traveler in Bejing flies To Lhasu, then (C) first flew to Chengdu.

Keyboard123

@castrone For reference, here were my translations for the first sentences in the answer choices too. I imagine we will get the same translations there too. Unless proven otherwise, I really think this rule has potential because it saves a lot of headache when dealing with double group 3 and 4 words in the same sentence.

"A doctor cannot prescribe porozine for a patient without first prescribing anthroxine for that patient.
A = A doctor
B = prescribe porozine for a patient
C = first prescribing anthroxine for that patient
Rule: AB --> C
Translation: If (AB) a doctor prescribed porozine for a patient, then (C) they first prescribed anthroxine for that patient.

"An ice sculpture artist cannot reach the yellow level of achievement without first achieving the green level."
A = An ice sculpture artist
B = reach the yellow level of achievement
C = first achieving the green level
Rule: AB --> C
Translation: If (AB) an ice sculpture artist reached the yellow level of achievement, then (C) they first achieved the green level.

"One cannot properly identify a mushroom without first examining its spores."
A = One
B = Properly identify a mushroom
C = Examining its spores
Rule: AB --> C
Translation: If (AB) one properly identifed a mushroom, then (C) they examined its spores.

Keyboard123

@phosita_phoeatah I think that's a fine way to approach this specific problem, but as you noted, it can get tricky when dealing with the opposite direction and you might also get a headache trying to obtain the contrapositive and "take up brain space" (I could be wrong about this).

As for the OT part I'm sure it wouldn't be hard to come up with a different symbol, maybe instead of a ">" at the end of your line (-->) you draw a triangle or something instead of the two lines. It wouldn't cost you too much time/ brain space to do so since you would only lift the pen once.

castrone

@Keyboard123 I mean sure. at a point its just arguing semantics and preference. the only thing that matters is getting what goes before and after the arrow correct