negate: All cows eat grass.

Question

negating sentences in graduate math 

Answer 1

Negation:  There exists at least one cow that does not eat grass.

 

I want to point out a common mistake.  Someone might answer "All cows do not eat grass."  But that is not the negation of the original proposition that "all cows eat grass."  The way to negate a universal claim about the objects in a set is to state there exists at least one object in the set that does not satisfy the universal claim.

Answer 2

Not all cows eat grass.