[generally]

I respectfully disagree. As a mathematician, I can tell you that in formal logic, these two sentences imply nothing unless you already know whether one of the conditions is true. (I hate to play the "expert" card and say trust me, but the short version is that until we know for sure about one of them, we know nothing about the other.) https://en.wikipedia.org/wiki/First-order_logic (long explanation of logic) https://en.wikipedia.org/wiki/Material_conditional#Truth_table (truth table) So in the table p q p → q T T T T F F F T T F F T p = RR is dirty q = Mueller is dirty p → q says if RR is dirty then Mueller is dirty. so in the table it shows us that Line 1. the statement is TRUE if both are dirty Line 2. the statement is FALSE if RR is dirty but Mueller is not Line 3. the statement is TRUE if RR is NOT dirty but Mueller is Line 4. the statement is TRUE if both are dirty q → p is the same with RR and Mueller swapped. So Q is telling us the truth if they are both dirty. He is also telling us the truth if they are both NOT dirty. ... or of course Q could be giving us disinformation and this all goes out the window. Bottom line: Both clean OR both dirty. Another discussion is whether the Q team is trained in formal logic. I believe that at least one member of the team is, and possibly is a mathematician or has at least studied logic. There is evidence of a strong cryptographic background on the team and that points to high level math skills.

[Cletus.D.Yokel]

Fine. But, “not dirty” is not stated, only dirty.

There is no evidence of Line 3 or 4 in the Q-drop.

[generally]

Ugh. Sorry.

All of my formatting was destroyed, apparently because I put in the arrow character.

Dang.

[generally]

I respectfully disagree.

As a mathematician, I can tell you that in formal logic, these two sentences imply nothing unless you already know whether one of the conditions is true.

(I hate to play the "expert" card and say trust me, but the short version is that until we know for sure about one of them, we know nothing about the other.)

https://en.wikipedia.org/wiki/First-order_logic (long explanation of logic)

https://en.wikipedia.org/wiki/Material_conditional#Truth_table (truth table)

So in the table

p q p → q

T T T

T F F

F T T

F F T

p = RR is dirty q = Mueller is dirty p → q says if RR is dirty then Mueller is dirty. so in the table it shows us that

Line 1. the statement is TRUE if both are dirty

Line 2. the statement is FALSE if RR is dirty but Mueller is not

Line 3. the statement is TRUE if RR is NOT dirty but Mueller is

Line 4. the statement is TRUE if both are dirty q → p is the same with RR and Mueller swapped.

So Q is telling us the truth if they are both dirty. He is also telling us the truth if they are both NOT dirty. ... or of course Q could be giving us disinformation and this all goes out the window.

Bottom line: Both clean OR both dirty.

Another discussion is whether the Q team is trained in formal logic. I believe that at least one member of the team is, and possibly is a mathematician or has at least studied logic. There is evidence of a strong cryptographic background on the team and that points to high level math skills.