Negation Problem Homework Help

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Homework Help Overview

The problem involves negating the statement "Only some of the students of the class are here today." The discussion centers around the interpretation of the terms used and the logical implications of the statement.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the meaning of "some" and its implications for the original statement. There are questions about how to express the statement in logical form and the effect of removing the word "only." Some participants propose that the negation could imply either no students or all students are present.

Discussion Status

The discussion is active, with participants sharing their interpretations and questioning the ambiguity of the terms involved. Some guidance is offered on how to approach writing the original statement in logical form, but there is no explicit consensus on the interpretations or the negation.

Contextual Notes

Participants note the ambiguity in language and the subjective nature of interpreting the statement, which may affect the understanding of "some" and "only." There is a recognition that the original statement's meaning could change based on these interpretations.

Mr Davis 97
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Homework Statement


Negate the following: Only some of the students of the class are here today.

Homework Equations

The Attempt at a Solution


Is the negation of this statement that either no students are in class or all students are in class?
How would I write the original statement in logical form?
Finally, would the original statement change at all if we removed the "only?"
 
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My interpretation is, that only some means not all but at least two, and some alone would mean possibly all, but this is tricky and by no means unambiguous. language usually isn't 100% clear. How would you write the original statement in logical form?
 
Define "some" and we can talk. Otherwise, this is an ambiguous question.
 
Mr Davis 97 said:
Is the negation of this statement that either no students are in class or all students are in class?
Yes, in my opinon.

How would I write the original statement in logical form?
You could try writing your answer and then negating it.

Finally, would the original statement change at all if we removed the "only?"

In this context, I interpret the "only" to mean "not all", so, yes, it would change the interpretation provided we don't interpret "some" to imply "not all" by itself.

However, as others have said, there are subjective aspects to interpreting the original statement..
 

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