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...

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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).


a) Berries are ripe along the trail, but grizzly bears have not been seen in the area.


b) Grizzly bears have not been seen in the area and hiking on the trail is safe, but berries are ripe along the trail.


c) If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been seen in the area.


d) It is not safe to hike on the trail, but grizzly bears have not been seen in the area and the berries along the trail are ripe.


e) 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.


f) Hiking is not safe on the trail whenever grizzly bears have been seen in the area and berries are ripe along the trail.



Answered Same DayDec 24, 2021

Answer To: Let p, q, and r be the propositions p : Grizzly bears have been seen in the area. q : Hiking is safe...

Robert answered on Dec 24 2021
127 Votes
554593-7
Consider 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
(a)
Berries are ripe along the trail, but grizzly bears have not been seen in the area.
Logical symbol for but is
Ù
.
Logical preposition of grizzly bears have not been seen in the area is
p
:
.
Thus,
rp
Ù
:
: Berries are ripe along the trail, but grizzly bears have not been seen in the area.
(b)
Grizzly bears have not been seen in the area and hiking on the trail is safe, but berries are ripe along the trail.
Logical preposition of Grizzly bears have not been seen in the area is
p
:
.
Logical symbol for but is
Ù
and logical symbol for and is
Ù
.
Thus,
(
)
pqr
ÙÙ
:
: Grizzly bears have not been seen in the area and hiking on the trail is safe, but berries are ripe along the trail.
(c)
If berries are ripe along the trail, hiking...
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