Question from a fried brain: difference between not both statement and always apart biconditional?

Comments

• Rachel Yoon Member

  September 2016 edited September 2016 173 karma

  I think yes for the box with a no slash, since A->/B and A<->/B both mean that if there is A, B can't be there. But in case of A<->/B, if B is not there, A should be there, and if A is not there, B should be there so either one of them should be there. So A or B should be in, but both can't be in.
  
  But in case of A->/B, if B is not there, it's a necessary condition, so nothing happens, it means it's ok for both A and B are out, I guess.
• 2 Likes

  abisin1234 Alum Member

  September 2016 edited September 2016 171 karma

  A->/B Allows for only 3 situations:
  1. A is in (where B is out)
  2. B is in (where A is out)
  3. Both are out.
  
  A<->/B Allows for 2 situations
  1. A is in (where B is out)
  2. B is in (where A is out)
  because of the double arrow, the rule flows in either direction (so your necessary is also your sufficient) so by having /B (where the relationship would normally fall away, leaving A to "float" instead having /B forces A to be in.
  
  
  If my knowledge serves me well
  
  So when you're drawing your in/out game board, you can properly infer for the first case that one of the out group slots will be occupied by either A/B (or both and therefore 2 slots)
  
  Whereas on your game board for the second scenario you can properly infer that one slot will be filled on both the in AND out group.
  
  These are my favourite rules because they make games so much easier (but only if you can figure it out from the language the rule is provided in.)
  
  Hope that helps!
• Cant Get Right Yearly + Live Member Sage ⭐ 🍌 7Sage Tutor

  September 2016 27900 karma

  
  

  @abisin1234 said:
  If my knowledge serves me well
  

  It does:)