Which one of the following CANNOT be the complete color combination of the glass in one of the windows?

Angelica on July 10 at 05:37PM

Orange & Purple

I'm confused about the orange and purple. I thought they couldn't go together and I still don't understand why they must go on every window.

1 Reply

Shunhe on July 11 at 02:55AM

Hi @Angelicagcd,

Thanks for the question! So take a careful look at the rule concerning purple and orange. If a window doesn’t have purple glass, then that window contains orange glass. Does that mean that purple and orange glass can’t go together? No, actually, it means that no window can have neither. Because if it has purple glass, then obviously it has purple glass. But if it doesn’t have purple glass, it has orange glass. And a window could have purple and orange glass based on the last rule, that’s totally possible as well. Diagramming the last rule gives us

~P —> O

And taking the contrapositive gives us

~O —> P

So each window has to have at least either O or P, and potentially both. So they can definitely go together, and the last rule is the reason at least one has to be on every window.

Hope this helps! Feel free to ask any other questions that you might have.