15. Let the predicate knows(x, y) again denote that person x knows person y, and happy(x) to mean that person x is happy. Which one of the following first order logic formulas encodes the claim “Every happy person knows somebody who is not happy"? (a) V x : happy(x) =→ 3 y:(knows(x, y) → happy(y)) (b) ▼ x : 3 y: (happy(x) ^ knows(x, y)) =-happy(y) (c) 3 x: V y: happy(x, y) = knows(x,y) (d) ▼ x: 3 y:¬happy(x) V ( knows(x, y) ^ -happy(y))
15. Let the predicate knows(x, y) again denote that person x knows person y, and happy(x) to mean that person x is happy. Which one of the following first order logic formulas encodes the claim “Every happy person knows somebody who is not happy"? (a) V x : happy(x) =→ 3 y:(knows(x, y) → happy(y)) (b) ▼ x : 3 y: (happy(x) ^ knows(x, y)) =-happy(y) (c) 3 x: V y: happy(x, y) = knows(x,y) (d) ▼ x: 3 y:¬happy(x) V ( knows(x, y) ^ -happy(y))
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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Transcribed Image Text:15. Let the predicate knows(x, y) again denote that person x knows person y, and happy(x) to mean that
person x is happy. Which one of the following first order logic formulas encodes the claim "Every happy
person knows somebody who is not happy"?
(a) V x : happy(x)= 3 y:( knows(x, y) = happy(y))
(b) x: у: (hаppу(x) Л kпows(х, у)) %— -һарру(у)
(с) Э х: у:happy(x, у) 3 knows(x, y)
(d) V x: 3 y:-happy(x) V ( knows(x, y) ^ -happy(y))
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