Solution to 2.

 

The wheat will grow well only if there is enough rain and it neither hails nor gets too hot. Only if it gets too hot if and only if it does not hail will the tomatoes grow well. Therefore, the wheat and the tomotoes will not both grow well.

 

The basic statements are clearly:

W = The wheat will grow well.

R = There is enough rain.

H = It hails.

T = It gets too hot.

G = The tomatoes will grow well.

Substituting we get:

 

W only if R and neither H nor T.

Only if T if and only if not-H G.

Therefore, not both W and G.

 

For the first, we can group it like this:

W only if {R and (neither H nor T)}

This is not the only way this could be grouped, as the statement is logically ambiguous, but the meaning indicates that it should be grouped like this.

The second should be grouped like this:

Only if (T if and only if not-H) G.

The 'only if' is indicating a conditional. The statement following the 'only if' must be the consequent, and so the other statement, 'G', must be the antecedent.

The conclusion is easy:

Therefore, not (both W and G)

 

Putting these all into notation, we get:

 

w->{r&(~h&~t)}

g->(t<->~h)

.:~(w&g)