Implications True/False

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?

 

Sorry for reviving this thread a little late, but isn't 'The museum has not opened; so you cannot come in.' true? Because if the antecedent is false and the consequent--lady's proposition, then isn't it true? I am assuming both of the propositions(lady and visitor) are true.