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# What is the negation of "All students passed the final"?

Question #106195. Asked by jakesgirl88. (Jun 09 09 5:56 PM)

daBomb619

"Some of the students did not pass the final."

http://www.physicsforums.com/archive/index.php/t-129021.html

While it may be true that all of the students failed the final, we do not know for sure. Thus, the negation of an "all" statement is a "some" statement, and vice versa.

 Jun 09 09, 6:01 PM
Jon53

I would venture that the correct negation would be "Not all of the students passed the final". This would indicate some or none passed.

Sorry I have no reference on this one.

 Jun 10 09, 1:01 PM
Baloo55th

I would like to agree with Jon to an extent. However, a complete negation would be 'None of the students passed the final'. We do not know from the question whether a complete or partial negation is required. 'Some' is an intermediate state between 'all' and 'none' and cannot logically be a negation of BOTH of them. It is a denial, but not a negation. (One angel, two angels, three angels, four angels - darn it, why won't they keep still for a moment?)

 Jun 10 09, 1:49 PM

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