1.For hiking on the trail to be safe, it is necessary but not sufficient that be
ID: 2834351 • Letter: 1
Question
1.For hiking on the trail to be safe, it is necessary but not sufficient that berries not be ripe along the trail and for grizzle bears not to have been seen in the area.
2.Hiking is not safe on the trail whenever grizzle bears have been seen in the area and berries are ripe along the trail.
Please explain dont just give the answers
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).Explanation / Answer
(Every class uses different logical connector notation. In my answer ~ means "not", ^ means "and")
Conditional statements have sufficient and necessary conditions.
if x, then y = x ---> y = x is sufficient and y is necessary
sufficient ---> necessary
Pay attention to connector words like necessary, sufficient, if, then, and, but, or, not for negations, etc.
1. For hiking on the trail to be safe, then it is necessary but not sufficient that berries not be ripe and for grizzly bears not to have been seen in the area.
Pay attention to the word "but" this is the same as the logical "and" connector. Splitting the sentences up, we now have:
For hiking on the trail to be safe, then it is necessary that berries not be ripe and for grizzly bears not to have been seen in the area.
(q ---> (~r ^ ~p))
we also have:
For hiking on the trail to be safe, it is not sufficient that berries not be ripe and for grizzly bears not to have been seen in the area.
(~(~r ^ ~p) ---> q)
Remember these two statements were connected by the word "but." So we combine these two statements with the and connector.
( (q ---> (~r ^ ~p)) ^ ~((~r ^ ~p) ---> q)) is your final answer
2. Hiking is not safe on the trail whenever grizzly bears have been seen in the area and berries are ripe along the trail.
"Whenever" means the same as "if." What comes after "whenever" will be your sufficient condition.
Whenever grizzly bears have been seen in the area and berries are ripe along the trail.
(p ^ r) will be your sufficient condition
"Hiking is not safe", ~q, then follows as your necessary condition.
((p ^ r) ---> ~q) is your final answer
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