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Answer the following problems completely. 1. Determine whether the following uses AND or OR. If it is OR determine further if it is inclusive or exclusive. a. You can kill a vampire by exposing him to sunlight or driving a wooden stake through his heart. Suppose you drive a stake through the heart of a vampire at exactly sunrise? Is he still dead? b. You buy a car with a 3 year or 36,000 miles warranty. If more than 3 years pass and you drive the car more than 36,000 miles, is the warranty still expired? c. A restaurant offers "soup or salad" with their dinner special. Can you order both? 2. Prove the second De Morgan's

Answer the following problems completely. 1. Determine whether the following uses AND or OR. If it is OR determine further if it is inclusive or exclusive. a. You can kill a vampire by exposing him to sunlight or driving a wooden stake through his heart. Suppose you drive a stake through the heart of a vampire at exactly sunrise? Is he still dead? b. You buy a car with a 3 year or 36,000 miles warranty. If more than 3 years pass and you drive the car more than 36,000 miles, is the warranty still expired? c. A restaurant offers "soup or salad" with their dinner special. Can you order both? 2. Prove the second De Morgan's

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterA: Appendix
SectionA.3: Inequalities
Problem 11E
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Answer the following problems completely. 1. Determine whether the following uses AND or OR. If it is OR determine further if it is inclusive or exclusive. a. You can kill a vampire by exposing him to sunlight or driving a wooden stake through his heart. Suppose you drive a stake through the heart of a vampire at exactly sunrise? Is he still dead? b. You buy a car with a 3 year or 36,000 miles warranty. If more than 3 years pass and you drive the car more than 36,000 miles, is the warranty still expired? c. A restaurant offers "soup or salad" with their dinner special. Can you order both? 2. Prove the second De Morgan's Law: -(p V q) = (-p) ^ (-q). 3. Show that the statement s = (-p^ q) ^ (pq) is not a tautology. 4. Prove the distributive law: p V (q Ar) = (pVq) ^ (p Vr). 5. Suppose x is a student, y is a math course, and M(x,y) is the predicate "x will take y". Translate the following sentences into predicate notation: a. Every student will take Calculus. b. Every student will take a math course. c. Lora will take Calculus and Linear Algebra. d. There is a course that everybody will take. e. There is a course that nobody will take. f. Tom will take all math courses except Topology. 12
Transcribed Image Text:Answer the following problems completely. 1. Determine whether the following uses AND or OR. If it is OR determine further if it is inclusive or exclusive. a. You can kill a vampire by exposing him to sunlight or driving a wooden stake through his heart. Suppose you drive a stake through the heart of a vampire at exactly sunrise? Is he still dead? b. You buy a car with a 3 year or 36,000 miles warranty. If more than 3 years pass and you drive the car more than 36,000 miles, is the warranty still expired? c. A restaurant offers "soup or salad" with their dinner special. Can you order both? 2. Prove the second De Morgan's Law: -(p V q) = (-p) ^ (-q). 3. Show that the statement s = (-p^ q) ^ (pq) is not a tautology. 4. Prove the distributive law: p V (q Ar) = (pVq) ^ (p Vr). 5. Suppose x is a student, y is a math course, and M(x,y) is the predicate "x will take y". Translate the following sentences into predicate notation: a. Every student will take Calculus. b. Every student will take a math course. c. Lora will take Calculus and Linear Algebra. d. There is a course that everybody will take. e. There is a course that nobody will take. f. Tom will take all math courses except Topology. 12
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