If exactly three friends appear together in a photograph, then each of the following could be true EXCEPT:

Tucker on November 29, 2019

Contrapositive of rule three (If not Y, then R)

I understand that the contrapositive flips and negates the statement. But the rule states that Raimundo appears in every picture that Yakira does not appear in. I understand the contrapositive of that states Yakira appears in every photo that Raimundo doesn't, but logically that doesn't makes sense to me. Since the rule doesn't state that Raimundo ONLY appears in photos that don't have Yakira, why is it not possible that both Raimundo and Yakira are not in the photo?

1 Reply

Ben on November 29, 2019

Hi Tucker, thanks for the question!

Rule 3: R appears in every picture that Y does not appear in.

You correctly described the conditional reasoning in if, then terms.

NOT Y - > R
NOT R - > Y

This is an either/or rule meaning that at least one of the variables must be placed in. It is possible for both to be placed because if either R or Y is in, we do not know what happens with the other variable.

The reason that it isn't possible for both R and Y to not be in the photo is because the moment one of them is not in (either NOT R or NOT Y), then the condition triggers to put the other variable in.

Let me know if this was helpful and if you have any other questions.