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Express each of these propositions as an English sentence. а) р—9 b) ¬q+r c) q→¬r d) pV qV r e) (p→¬r) V (q →¬r) A (p^ q) v (¬q^ r) 3. 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 ber ripe along the trail. c) If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not seen in the area. d) It is not safe to hike on the trail, but grizzly bears have not been seen in the area a berries along the trail are ripe. e) For hiking on the trail to be safe, it is necessary but not sufficient that berries not

Express each of these propositions as an English sentence. а) р—9 b) ¬q+r c) q→¬r d) pV qV r e) (p→¬r) V (q →¬r) A (p^ q) v (¬q^ r) 3. 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 ber ripe along the trail. c) If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not seen in the area. d) It is not safe to hike on the trail, but grizzly bears have not been seen in the area a berries along the trail are ripe. e) For hiking on the trail to be safe, it is necessary but not sufficient that berries not

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Express each of these propositions as an English sentence. a) p→q b) ¬q+ r c) q→¬r d) pV qV r e) (p →¬r) V (q →¬r) f) (p^ q) v (¬q^ r) 3. 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.
Transcribed Image Text:Express each of these propositions as an English sentence. a) p→q b) ¬q+ r c) q→¬r d) pV qV r e) (p →¬r) V (q →¬r) f) (p^ q) v (¬q^ r) 3. 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.
Еxercise 4: 1. Let p and q be the propositions p: It is below freezing. q : It is snowing. Write these propositions using p and q and logical connectives (including negations). a) It is below freezing and snowing. b) It is below freezing but not snowing. c) It is not below freezing and it is not snowing. d) It is either snowing or below freezing (or both). e) If it is below freezing, it is also snowing. f) Either it is below freezing or it is snowing, but it is not snowing if it is below freezing. g) That it is below freezing is necessary and sufficient for it to be snowing. 2. Let p, q, and r be the propositions p:You have the flu. q :You miss the final examination. r:You pass the course.
Transcribed Image Text:Еxercise 4: 1. Let p and q be the propositions p: It is below freezing. q : It is snowing. Write these propositions using p and q and logical connectives (including negations). a) It is below freezing and snowing. b) It is below freezing but not snowing. c) It is not below freezing and it is not snowing. d) It is either snowing or below freezing (or both). e) If it is below freezing, it is also snowing. f) Either it is below freezing or it is snowing, but it is not snowing if it is below freezing. g) That it is below freezing is necessary and sufficient for it to be snowing. 2. Let p, q, and r be the propositions p:You have the flu. q :You miss the final examination. r:You pass the course.
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