Differences between negations of two similar statements? I want to negate the following two statements:
a) ‘some of the students in the class are not here today’
b) ‘only some of the students in the class are here today’
I think statement (a) negates to ‘all the students in the class are here today’. However, what about statement (b)?
Statement (b) seems to be equivalent to statement (a), so are the negations the same as well?
 A: In natural language, "some" is usually understood as "some but not all" (i.e. "only some"). Under this interpretation, sentences a) and b) are equivalent, and so are their negations.
Literally, or the way it is used in mathematics, "some" just means "at least one"; this is consistent with the possibility of "all", while "only some" excludes that possibility.
The negation of "some (= at least one and possibly all)" is "none". Hence the negation of the literal meaning of

a) Some of the students are not here today

is

None of the students are not here today

i.e.

All of the students are here today.

The negation of "only some" = "some and not all" is "not any or not not all" = "none or all". Hence the negation of

b) Only some of the students are not here today

is

None or all of the students are not here today

i.e.

All or none of the students are here today.

This is for the literal meaning as used in mathematics. Under the pragmatic interpretation of "some" as "only some", the negation of both sentences is the latter one.
A: One useful way to do this and get use to logic notation is thinking in the following way. Consider the first sentence
a) “Some of the students in the class are not here today”.
Let $U$ be the set of all the students in the class, and let $P(x)$ be the expression “Student $x$ is here today”.
Then the sentence a) is written as $(\exists x \in U): \neg P(x)$. Our goal is to negate this sentence.

Recall that $\neg [(\exists x \in U): P(x)] = (\forall x \in U): \neg P(x)$

So the negation of our sentence is
$$\neg [(\exists x \in U):\neg P(x)] = (\forall x \in U): \neg(\neg P(x)) = (\forall x \in U): P(x)$$
In English it would be something like “All of the students in the class are here today.”
Applying the same reasoning, you can now solve for the sentence b) (which I will left as an exercise).
Any doubt, please let me know.
