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Showing Revision 3 created 05/24/2016 by Udacity Robot.

  1. To answer this question, the very first thing we observe is that each statement implies itself.
  2. So we will draw every element of the diagonal as true.
  3. We also observe that "not pink" implies "green" is the same as pink or green.
  4. If you do the truth table, you find that this is true either if green is true, which will be the case of B as well,
  5. or if pink is true, in which case the precondition which is implied will be false, and therefore the entire statement is true.
  6. So we can find out that B is exactly the same as D.
  7. With that in mind, we answer the question for A to C first.
  8. Pink clearly implies that pink or green is true. It doesn't imply that pink and green is true, so C is not open.
  9. But because B is equivalent to D, we also check over here.
  10. Pink or green doesn't imply pink, because green might be true, and doesn't imply pink and green because green might be false.
  11. But it does imply D because D is exactly the same as B.
  12. Pink and green implies pink. It also implies pink or green.
  13. And since B is the same as D, implies D.
  14. And finally, for this one over here, we just copy over B. So we get this guy and this guy over here.