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2. Assuming the following predicates: L(x, y): x is strictly less than y (x0); • D(x, y): x divides y exactly; determine which of the following formulae are true (in your answer include an expres- sion of the formula in concise (good) English without variables). (a) VrEN. (D(2, x) → E(x)) (b) y N.V.x € N. L(x, y)

2. Assuming the following predicates: L(x, y): x is strictly less than y (x0); • D(x, y): x divides y exactly; determine which of the following formulae are true (in your answer include an expres- sion of the formula in concise (good) English without variables). (a) VrEN. (D(2, x) → E(x)) (b) y N.V.x € N. L(x, y)

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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2. Assuming the following predicates: • L(x, y): x is strictly less than y (x<y); • E(x): x is even; • P(x): x is a prime number; • EQ(x, y): x equals y (x=y); • G(x): x is greater than zero (x>0); • D(x, y): x divides y exactly; determine which of the following formulae are true (in your answer include an expres- sion of the formula in concise (good) English without variables). (a) Vx E N. (D(2,x) → E(x)) (b) y € N. V E N. L(x, y) (c) ExZ+. Vy ≤ Z+. (G(x) → (P(y) ^ L(x, y))) Next, using the above predicates and quantifiers were necessary, express the following English statements in logic. (d) "Any non-zero integer divides itself" (e) "A prime number's only positive factors are 1 and itself."
Transcribed Image Text:2. Assuming the following predicates: • L(x, y): x is strictly less than y (x<y); • E(x): x is even; • P(x): x is a prime number; • EQ(x, y): x equals y (x=y); • G(x): x is greater than zero (x>0); • D(x, y): x divides y exactly; determine which of the following formulae are true (in your answer include an expres- sion of the formula in concise (good) English without variables). (a) Vx E N. (D(2,x) → E(x)) (b) y € N. V E N. L(x, y) (c) ExZ+. Vy ≤ Z+. (G(x) → (P(y) ^ L(x, y))) Next, using the above predicates and quantifiers were necessary, express the following English statements in logic. (d) "Any non-zero integer divides itself" (e) "A prime number's only positive factors are 1 and itself."
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