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Let p, q, and r be the propositions

p : Grizzly bears have been seen in the area.

q : Hiking is safe on the trail.

r : Berries are ripe along the trail. Write these propositions using p, q, and r and logical connectives (including negations).

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.

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Recall that given any implication: a→b, we can translate this as saying

"a is a sufficient condition for b" or equivalently: "b is a necessary condition for a."

(1) For hiking to be safe (a:=q), the necessary condition (b:=¬r∧¬p) in your case is that berries not be ripe and for grizzly bears to not to have been seen in the area.

So we have q→(¬r∧¬p)

(2) However, you are explicitly told that this condition: (¬r∧¬p) is not sufficient, so you have to negate the converse of (1): you need to negate (¬r∧¬p)→q.

This gives us: ¬[(¬r∧¬p)→q]. 

To write the complete statement, you need the connective ∧ in between (1) and (2):

[q→(¬r∧¬p)]∧¬[(¬r∧¬p)→q].

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