# Implications True/False

1. Jan 13, 2009

### 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?

2. Jan 14, 2009

### MathematicalPhysicist

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.

3. Jan 14, 2009

### HallsofIvy

Staff Emeritus
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.

4. Jan 15, 2009

### MathematicalPhysicist

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

5. Jan 15, 2009

### HallsofIvy

Staff Emeritus
Then I must have misunderstood "and what the attendant says is false".

(Besides, I wasn't "reiterating", I was only "iterating".)

6. Apr 8, 2009

### razored

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.

Last edited: Apr 8, 2009