# Implications True/False

razored
From "Principles of Mathematics" by Allendorfer and Oakley.

"Discuss the reasoning of the 'visitor' in the following: An early visitor to a museum found the door open and walked in. An attendant said to him, 'The museum has not opened; so you cannot come in.' The visitor replied, 'If this museum has not opened, then I am not in,' and proceeded to look around."

For the visitors implication, 'If this museum has not opened, then I am not in,' is it meant that the first proposition is true and the second is false, so meaning it is entirely false. (A^B) If it is false, then why does he proceed to look around?

Gold Member
The reasoning is: "if he's in, then the museum has opened", and what the attendant says is false.
Now he's in, thus the museum is open, and he can keep roam around the museum.

Homework Helper
No, this does not imply that what the attendant said is false.

The visitor is interpreting "'The museum has not opened; so you cannot come in" as the implication you give, "'If this museum has not opened, then I am not in" and convertijng to the contra-positive, "If I am in, then the museum has opened". One is true if and only if the other is.

Gold Member
Reiterating me won't change the fact that my answer is correct. :-)