Negation Problem Homework Help

[Mr Davis 97]

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?"

 

[fresh_42]

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?

 

[member 587159]

Define "some" and we can talk. Otherwise, this is an ambiguous question.

 

[Stephen Tashi]

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..