I got part 1 wrong but can't seem to figure out why.
All farmers -> not all farmers, grow corn -> grow only corn. When I put it together it made sense. Am i missing something?
Write the negation of each of the following
1. All farmers grow corn.
Not all farmers grow only corn
2. Corn is grown only by farmers.
Corn can be grown by non-farmers (is it wrong to use the hypothetical stance "can be" in predicate logic)
I would read (2) as: for all corn, there exists a farmer that grows it.
So the negation says that there exists corn grown by someone other than a farmer.
This is a bit more precise than saying "can be." Just because corn can be grown by non-farmers doesn't mean it is actually grown by non-farmers. So your attempt at negating (2) does not actually contradict (2).