Implications True/False

  • Thread starter razored
  • Start date
  • #1
razored
173
0
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?
 

Answers and Replies

  • #2
MathematicalPhysicist
Gold Member
4,699
369
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
HallsofIvy
Science Advisor
Homework Helper
43,021
971
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
MathematicalPhysicist
Gold Member
4,699
369
Reiterating me won't change the fact that my answer is correct. :-)
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
43,021
971
Then I must have misunderstood "and what the attendant says is false".

(Besides, I wasn't "reiterating", I was only "iterating".)
 
  • #6
razored
173
0
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.

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:

Suggested for: Implications True/False

Replies
5
Views
415
Replies
16
Views
499
Replies
1
Views
431
Replies
14
Views
1K
  • Last Post
Replies
6
Views
1K
Replies
15
Views
639
Replies
2
Views
3K
Replies
1
Views
1K
Replies
8
Views
1K
Replies
8
Views
1K
Top