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6)For each of the following equivalences, determine if it is valid for all predicates P and Q. If valid then give a full explanation. If invalid then provide a counter example. (a) Vx(P(x) ^ Q(x)) = x²(x) ^ ¬³xQ(x) (b) \x(¬P(x) v Q(x)) = (¬ªxP(x)) v (vxQ(x)) (c) 3x, y (P(x) v Q (y)) = 3x (P(x) v Q(x)) (d) 3x, y (P(x) ^ ¬Q(x)) = ((3x(P(x))) ((())))

6)For each of the following equivalences, determine if it is valid for all predicates P and Q. If valid then give a full explanation. If invalid then provide a counter example. (a) Vx(P(x) ^ Q(x)) = x²(x) ^ ¬³xQ(x) (b) \x(¬P(x) v Q(x)) = (¬ªxP(x)) v (vxQ(x)) (c) 3x, y (P(x) v Q (y)) = 3x (P(x) v Q(x)) (d) 3x, y (P(x) ^ ¬Q(x)) = ((3x(P(x))) ((())))

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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)For each of the following equivalences, determine if it is valid for all predicates P and Q. If valid then give a full explanation. If invalid then provide a counter example. (a) \x(P(x) ^ Q(x)) = \xP(x) ^ ¬³xQ(x) (b) Vx(P(x) v Q(x)) = (-3xP(x)) v (vxQ(x)) (c) 3x, y (P(x) v Q (y)) = 3x (P(x) v Q(x)) (d) 3x, y (P(x) ^ ¬Q(y)) = ((3x(P(x)))^((())))
Transcribed Image Text:)For each of the following equivalences, determine if it is valid for all predicates P and Q. If valid then give a full explanation. If invalid then provide a counter example. (a) \x(P(x) ^ Q(x)) = \xP(x) ^ ¬³xQ(x) (b) Vx(P(x) v Q(x)) = (-3xP(x)) v (vxQ(x)) (c) 3x, y (P(x) v Q (y)) = 3x (P(x) v Q(x)) (d) 3x, y (P(x) ^ ¬Q(y)) = ((3x(P(x)))^((())))
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