Diagram Help: If C does not occur, then A and B cannot both occur

Comments

• Slow is Fast Alum Member

  April 2021 edited April 2021 445 karma

  I think this is embedded logic, but hopefully someone else can correct me if I'm wrong.

  There's a basic "If x then y" statement, so we know there's going to be a "-->" relationship between the two sides.
  "If C does not occur" is simple to diagram: /C

  The latter part "then A and B cannot both occur" is by itself a conditional logic statement: A --> /B

  So now we just combine the two pieces together with the arrow: /C --> (A --> /B). We want the statement to read as, "If not C, then (this relationship between A & B )." The relationship between A & B just happens to be a not-both.
• yunonsie Member

  April 2021 611 karma

  @obloome Ahhh that's a great point, I missed that! But could you still write it as [/C > /A & /B]? Like functionally, would both statements affect a game in identical ways? Or should I go back to that embedded lesson....
• 1 Like

  Slow is Fast Alum Member

  April 2021 edited April 2021 445 karma

  @yunonsie Hm, I don't think they're the same statements.

  Let's look at your statement first: /C --> /A & /B.
  "And" statements in the necessary can be split. So we could split this to say:
  /C --> /A
  AND
  /C --> /B

  This means that whenever we have /C, we never have A AND we never have B. That is, A and B are both out in the world of /C.*

  Cool. Now let's look at this other one /C --> (A --> /B) and again assume that we have /C so that the necessary is triggered. In this situation, we actually have three different options that can happen in the "/C universe" because of the not-both logic.
  1. A --> /B (A in, B out)
  2. B --> /A (B in, A out)
  3. A and B both out *(which is what your statement said)

  Your original statement captures only one of the three worlds inherent in the not-both relationship. If you only wrote the statement as #3, then you'd be forgetting the first two possibilities on a game where either A or B could be in.

  We don't want A and B to be out forever and always. We just don't want them to be in together.
• yunonsie Member

  April 2021 edited April 2021 611 karma

  @obloome Thank you! SO helpful!
• matiecena83 Member

  April 2021 62 karma

  @obloome Thank you!
• Slow is Fast Alum Member

  April 2021 445 karma

  @yunonsie @matiecena83 no problem! Never thought I'd get to a point where I knew enough to answer questions yet here we are, lol. Glad it was helpful.