Disjunction Question

uh1999
Posts: 39
Joined: Wed Dec 21, 2011 11:20 am

Disjunction Question

Postby uh1999 » Mon Feb 13, 2012 7:37 pm

During my study of disjunctions, I came across this question:

Greg claims, "I returned the book to the library on Monday night or Tuesday morning." If Greg returned the book on Tuesday afternoon, then his claim is false.

A. Valid
B. Invalid
C. Unknown

I chose A, because in order to negate an "or," all of the elements (Monday night, Tuesday morning, and Monday night and Tuesday morning) must be negated. If he turned the book in on Tuesday afternoon, then he didn't turn it in on Monday night, Tuesday morning, or Monday night and Tuesday morning.

The correct answer is C, because Tuesday afternoon only negates one of the elements (i.e., Monday night and Tuesday morning). It does not negate the remaining two elements Monday night or Tuesday morning.

I don't know why the answer choice is C.

Can someone explain why?

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KevinP
Posts: 1324
Joined: Sat Sep 26, 2009 8:56 pm

Re: Disjunction Question

Postby KevinP » Mon Feb 13, 2012 8:48 pm

uh1999 wrote:During my study of disjunctions, I came across this question:

Greg claims, "I returned the book to the library on Monday night or Tuesday morning." If Greg returned the book on Tuesday afternoon, then his claim is false.

A. Valid
B. Invalid
C. Unknown

I chose A, because in order to negate an "or," all of the elements (Monday night, Tuesday morning, and Monday night and Tuesday morning) must be negated. If he turned the book in on Tuesday afternoon, then he didn't turn it in on Monday night, Tuesday morning, or Monday night and Tuesday morning.

You make the assumption that he can only return the book once. It may be that possible he could have checked the book out and returned it Monday morning, rechecked the book out and returned it Tuesday morning, and then re-rechecked the book out and returned it Tuesday afternoon.

uh1999 wrote:The correct answer is C, because Tuesday afternoon only negates one of the elements (i.e., Monday night and Tuesday morning). It does not negate the remaining two elements Monday night or Tuesday morning.

Tuesday afternoon actually doesn't negate any of the elements unless you assume, of course, that he can return the book only once. In this case, that seems to be an unwarranted assumption.


I found a similar example on this site:
To determine if an "or" claim is true or not, we must be able either to affirm one of the elements, or negate all of them. In this case, "Tuesday afternoon" only negates "Monday night" and "Tuesday morning" if you assume John can return the book only once--something we are not told. Because John may have returned the book both Monday night and Tuesday afternoon, for example, affirming that he did return it Tuesday afternoon does not rule out the possibility that he also returned it earlier.

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