Biconditionals

Comments

• DumbHollywoodActor Alum Inactive ⭐

  November 2016 edited November 2016 7468 karma

  Yes. that’s true.
  
  I like JY’s approach:
  
  For A<--->/B or /A <--> B or /B <--> A or B<-->/A, A and B are always apart.
  
  For A <--> B or B<--> A, A and B are always together.
  
  That tends to keep things clear for me.
• M.Yanka106 Member

  November 2016 113 karma

  I think one is the contrapositive of the other. As described in the comment above, it conveys the idea that the 2 pieces are always apart. Here is how:
  
  (1) /J ----> L = /L ------> J (2) (either or)
  
  (3) J ------>/L = L ------> /J (4) (not both)
  
  If you look at representations (1) and (4), you will see that the arrow is going back and forth (so to speak). Same for (2) and (3). Thus, if you find two separate statements or a statement with "either or.... not both" in it, you can set it up this way and conclude that the pieces are forever apart.
  
  Hope that helps. If I am wrong, I am sure @DumbHollywoodActor will let us both know.
  
• wilderness Alum Member

  November 2016 133 karma

  Yes.
  
  /J<->L breaks down into two conditionals:
  
  (1) /J --> L
  (2) L --> /J
  
  Let's take the contrapositives of each.
  
  (1b) /L --> J
  (2b) J --> /L
  
  We can combine (1b) and (2b) to form the following biconditional:
  
  (2) /L <-> J , or as you put it, J <-> /L
  
  We can do this because contrapositives are logically equivalent propositions.