Ensuring Safe Hiking: The Importance of Ripe Berry and Grizzly Bear-Free Trails

[Bashyboy]

The compound proposition is, "For hiking on the trail to be safe, it is necessary but not
sufficient that berries not be ripe along the trail and for grizzly bears not to have been seen in the area."

where:
p:Grizzly bears have been seen in the area.
qiking is safe on the trail.
r:Berries are ripe along the trail.

I wrote my answer as (\neg r \wedge \neg p)\rightarrow q

But the answer is (q→(¬r∧¬p))∧¬((¬r∧¬p)→q)

I honestly don't see this as being the answer. Please help.

 

[Bashyboy]

Bump.

 

[haruspex]

I wrote my answer as (\neg r \wedge \neg p)\rightarrow q

I read that as saying it is a sufficient condition: If no ripe berries and no bears seen then it is safe. For the necessity part, try rewording the given expression in the form "if ... then it is unsafe".