The use of "unless" Group 3 and "cannot" Group 4 combined translation in a Sequencing LG

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• 1 Like

  Justicerequiresconsequences Core Member

  June 2021 187 karma

  Review Introduction to Logic, section 45 questions for the translation rules and practice questions. This will clear this up. You can use either one, but you must follow the methodology or you will get turned around, or at least confused. Look at, and do several of the problems to get this clear.
• 1 Like

  LawBound-1 Yearly Member

  June 2021 edited June 2021 90 karma

  Hi, here is the explanation by JY: https://7sage.com/lesson/group-3-group-4/.

  First, you have to remember that when you pick a group, the other logical indicator becomes a negation. Meaning that the used indicator/group you are using variable will be left alone and whatever the unused indicator/group you are not using variable will be negated.

  So, if I pick Group 3 (W) than J's "Cannot" = /, which means I have / J & W
  W is left alone because it's following the Group I am using and J is part of the group I did not choose so it gets negated.

  If I pick Group 4 (J) than W's "Unless" = /, which means I have J & / W
  J is left alone because it's following the Group I am using and W is part of the group I did not choose so it gets negated.

  Group 3:

  Cannot select J unless W is also selected

  1. Find variables (In this case because I chose Group 3, I will leave the W alone (because it follows unless) and apply the negation to the J which is indicated by the "cannot", "cannot" = /)

  So, I have:
  / J W

  1. Apply Group 3 Rule (pick variable J, negate it, make it sufficient)

  J - W

  Contrapositive: / W - / J

  Group 4:

  Cannot select J unless W is also selected

  1. Find variables (In this case because I chose Group 4, I will leave the J alone (because it follows the "Cannot") and apply the negation to the W which is indicated by the "unless", "unless" = /)

  So, I have:
  J / W

  1. Apply Group 4 Rule (pick variable W, negate it, make it necessary)

  J - W

  Contrapositive: / W - / J

  Hope that helps!
• bearwithnohoney Member

  June 2021 edited June 2021 71 karma

  
• bearwithnohoney Member

  June 2021 71 karma

  This definitely helps! I also just reviewed those lessons as per your suggestions and they definitely cemented that for me. Thank you. I typically choose the Group 3 version for some reason my brain just gravitates toward automatically negating the sufficient and going with that. Glad to see they are interchangeable logically (been a while since I took that lesson)

  I suppose my second issue is extracting LG inferences from them when they involve spatial elements like "H cannot be shown earlier than 3 unless I is shown in 1." = "H is after 3 if I is 1" type stuff. Maybe the solution is to just find conditional games and drill them until it clicks

  Thank you guys for your help. Also anyone reading this thread feel free to chime in if you struggle too and/or have found some awesome ways to go about locking these down in LG's. Cheers!
• 2 Likes

  Jordan Johnson Member ⭐

  June 2021 edited June 2021 686 karma

  @bearwithnohoney
  I like to simplify my conditionals as best I can. So this statement:
  "Hanbock cannot be shown earlier than the third week unless Ibex is shown in the first week"
  ... can be translated to:
  "H can be shown earlier than the third week only if I is shown in the first week"

  (When I see an 'unless', I always negate the sufficient and change 'unless' to 'only if' when I see the term. It's quicker than trying to decide which thing to negate on-the-fly.)

  That should produce the following, assuming multiple variables can be in the same spot:
  " H_1/2 --> I_1" (aka "H can be in 1 or 2 [or both] only if I is in 1").

  Hope that helps!
• Jordan Johnson Member ⭐

  June 2021 edited June 2021 686 karma

  [duplicate post]
• 1 Like

  LawyeringForLife-1 Member

  June 2021 edited June 2021 279 karma

  Cannot...Unless is super common on LG and honestly, I translate these only when it's group 3 or group 4 independently.
  Group 3+4 are the easiest to handle because they cancel each other out, so you just drop them:

  Cannot - negative
  unless = if not - negative
  2 negatives make a positive

  So:
  x cannot be in group 1 unless y is in group 1
  x cannot be in group 1 unless y is in group 1
  x in group 1, y in group 1

  This is equivalent to all these:
  IF x in group 1, THEN y in group 1
  x in group 1, ONLY IF y in group 1

  Hope it helps.

  And in regard to the inferences - I have been in the same boat - drilling games with conditionals is key, but find games that JY splits the board and force yourself to do them just by using the conditional chain. PT43 G3 is not too difficult, but good practice.
  I really like PT41 G3 - it has 2 bi-conditional and it was a real cluster for me in the beginning. JY solves it with 4 boards leveraging the bi-conditionals - do it just following the chain.
• bearwithnohoney Member

  June 2021 71 karma

  @"Jordan Johnson" said:
  @bearwithnohoney
  I like to simplify my conditionals as best I can. So this statement:
  "Hanbock cannot be shown earlier than the third week unless Ibex is shown in the first week"
  ... can be translated to:
  "H can be shown earlier than the third week only if I is shown in the first week"

  (When I see an 'unless', I always negate the sufficient and change 'unless' to 'only if' when I see the term. It's quicker than trying to decide which thing to negate on-the-fly.)

  That should produce the following, assuming multiple variables can be in the same spot:
  " H_1/2 --> I_1" (aka "H can be in 1 or 2 [or both] only if I is in 1").

  Hope that helps!

  That's brilliant!
• bearwithnohoney Member

  June 2021 71 karma

  @"M.Y.M.M.Y.M." said:
  Cannot...Unless is super common on LG and honestly, I translate these only when it's group 3 or group 4 independently.
  Group 3+4 are the easiest to handle because they cancel each other out, so you just drop them:

  Cannot - negative
  unless = if not - negative
  2 negatives make a positive

  So:
  x cannot be in group 1 unless y is in group 1
  x cannot be in group 1 unless y is in group 1
  x in group 1, y in group 1

  This is equivalent to all these:
  IF x in group 1, THEN y in group 1
  x in group 1, ONLY IF y in group 1

  Hope it helps.

  And in regard to the inferences - I have been in the same boat - drilling games with conditionals is key, but find games that JY splits the board and force yourself to do them just by using the conditional chain. PT43 G3 is not too difficult, but good practice.
  I really like PT41 G3 - it has 2 bi-conditional and it was a real cluster for me in the beginning. JY solves it with 4 boards leveraging the bi-conditionals - do it just following the chain.

  That's an excellent way to retrain yourself via omission of "cannot" and "unless". I like that a lot. I will def check that game out. I haven't taken anything in the 40's so this is perfect for me. Thanks for your help