# If the complete color combination of the glass in one of the windows is purple, rose, and orange, then the complete c...

on August 4 at 03:07AM

purple and Orange

in Rule 4 it says if a glass does not contain purple glass then it contains orange glass. doesn't that mean that purple and orange can't be in the same window? If so, how can the question be if the glass contains purple, orange and rose? What am I missing with this question? I don't get it.

Skylar on August 4 at 01:39PM

@shannonk68, happy to help!

You are correct that Rule #4 says if a glass does not contain purple, then it must contain orange. However, you are incorrect in interpreting this to mean that purple and orange cannot be assigned to the same window. Instead, Rule #4 means that at least one of orange or purple - and possibly both orange and purple - must be in each window.

We can diagram Rule #4 and its contrapositive as:
not P -> O
not O -> P

Notice how O and P are the necessary conditions in this diagram. Since they are not sufficient, we don't know what has to or cannot happen when we have O or when we have P. We only know that when we don't have P we must have O and when we don't have O we must have P. This is a classic Either/Or scenario, as we must always have either O or P or possibly both in. Therefore, it is entirely possible to have both O and P assigned to the same window as we see in this question.

Does that make sense? Please let us know if you have any other questions!