Let p, q, and r be the propositions p: Grizzly bears have been seen in the area.

Question

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 c. If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not beern d. It is not safe to hike on the trail, but grizzly bears have not been seen in the area and the e. For hiking on the trail to be safe, i is necessary but not sufficient that berries not be ripe ripe along the trail. seen in the area. berries along the trail are ripe along the trail and for grizzly bears not to have been seen in the area.

Explanation / Answer

Answer is as follows :

a)

r(x) ? ¬ p(x)

b)

(¬ p(x) ? q(x) ) ? r(x)

c)

r(x) ? ( q(x) ? p(x) )

d)

¬ q(x) ? ( ¬ p(x) ? r(x) )

e)

( ¬ r(x) ? ¬ p(x) ) ? q(x)

" ? " is used for BUT NOT

" ? " is used for AND , BUT

" ¬ " is used for NOT

" ? " is used for IF AND ONLY IF

" ?" is used for IF THAN

if there is any query please ask in comments...

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