1 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 B 1 (77.93 KiB) Viewed 54 times
1 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 B 2 (38 KiB) Viewed 54 times
1) 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 c) If berries are ripe along the trail, hiking is safe if and only if grizzly bears have not been seen in the area. the area. 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.
2) State the converse, contrapositive, and inverse of each of these conditional statements. a) If it snows today, I will ski tomorrow. b) I come to class whenever there is going to be a quiz. c) A positive integer is a prime only if it has no divisors other than 1 and itself.
4) Construct a truth table for each of these compound propositions. a) p→→q b) b) →p → 9 c) (p →q) v (p →q) d) (p →q) ^ (p → q) 5) Construct a truth table for each of these compound propositions. a) p→ (qvr) b) p→ (q→ r) c) (p →q) v (pr)
6) Construct a truth table for (p↔ q) → (r↔s).
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