Discrete Mathematics

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 the following propositions using p, q, and r and logical operators.

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

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

(c) For hiking on the trail to be safe, it is necessary that berries not be ripe along the trail and for grizzly bears not to have been seen in the area.

Answer 1

A) not p and Q and R

B) R --> ( Q <--> not P)

C) (R and not P) <--> Q