Which of the following is a negation of the statement below?

All students like math.

All students do not like math.
No students do not like math.
Some students like math.
All students like science.

Question

Which of the following is a negation of the statement below?

All students like math.



All students do not like math.
No students do not like math.
Some students like math.
All students like science.

anonymous · Answer

i am willing to bet you can think about this without thinking in terms of math

anonymous · Answer

i just like making sure

anonymous · Answer

suppose it is not true 
that is it is not true that all students love math
how would you prove this?

anonymous · Answer

all you need to do is come up with one student that does not like math

anonymous · Answer

thats not from the choices

anonymous · Answer

oh, then i am confused
i would say the negation is "some student does not like math"

anonymous · Answer

in fact, i do not see the answer from the choices that i like, so i will let some one else answer 
All students do not like math. is wrong  since all we need is one that does not like math, not all
No students do not like math. is wrong because this says the same thing as "all students like math"
Some students like math. is wrong because "some" could mean "all"
All students like science. is silly

where does this question come from?