Discrete

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. 4. Let A = (0, 2, 4, 6, 8, 10), B = {0,1,2,3,4,5,6), and C = {4,5,6,7,8,9,10). Write the elements and draw the Venn diagram of the combinations of the sets A, B, and c: a) ABC. b) (AUB) c) AUBUC d) (AB) UC. 5. Show that each of these conditional statements is a tautology by using truth tables. a)-(p) +9 b) (49) (p) 6. Show that pq and (p/q) V(-p) are logically equivalent. 7. Show that (p => q) and pt. are logically equivalent