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
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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