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Suppose L (f1, f2, 9, $, c) is a first-order language where f1, f2 are binary function symbols, g is a unary function symbol, o is a binary predicate symbol and c is a constant symbol. Consider the usual structure of the number theory as an L-structure N = (N,+, x, S, <, 0) by the following interpretations: f" is + (the addition function), fg' is x (the multiplication function), g" is S (the successor function), o" is < (the usual order relation) and c" is the number 0. (a) What is the interpretation of the term f1(g(g(c)), f2(g(x), y)) in N, where xn is 2 and yn is 3? Show your work. (b) Find the value of the A", where A is the L-formula 1 (3x)(Vy)f2(x, y) = y. (c) Write an L-formula B(x) with a free variable x such that N = B(n) iff n is an odd number.

Suppose L (f1, f2, 9, $, c) is a first-order language where f1, f2 are binary function symbols, g is a unary function symbol, o is a binary predicate symbol and c is a constant symbol. Consider the usual structure of the number theory as an L-structure N = (N,+, x, S, <, 0) by the following interpretations: f" is + (the addition function), fg' is x (the multiplication function), g" is S (the successor function), o" is < (the usual order relation) and c" is the number 0. (a) What is the interpretation of the term f1(g(g(c)), f2(g(x), y)) in N, where xn is 2 and yn is 3? Show your work. (b) Find the value of the A", where A is the L-formula 1 (3x)(Vy)f2(x, y) = y. (c) Write an L-formula B(x) with a free variable x such that N = B(n) iff n is an odd number.

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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Please give correct answer for a, b and c. Thanks.

Suppose L = (f1, f2, 9, Ø, c) is a first-order language where f1, f2 are binary function symbols, g is a unary function symbol, o is a binary predicate symbol and c is a constant symbol. Consider the usual structure of the number theory as an L-structure N = (N,+, x, S, <,0) by the following interpretations: fª is + (the addition function), f is x (the multiplication function), g" is S (the successor function), o" is < (the usual order relation) and c" is the number 0. (a) What is the interpretation of the term fi(g(g(c)), f2(g(x), y)) in N, where x" is 2 and y" is 3? Show your work. (b) Find the value of the A", where A is the L-formula (3x)(Vy)f2(x,y) = y. (c) Write an L-formula B(x) with a free variable x such that N = B(n) iff n is an odd nитber.
Transcribed Image Text:Suppose L = (f1, f2, 9, Ø, c) is a first-order language where f1, f2 are binary function symbols, g is a unary function symbol, o is a binary predicate symbol and c is a constant symbol. Consider the usual structure of the number theory as an L-structure N = (N,+, x, S, <,0) by the following interpretations: fª is + (the addition function), f is x (the multiplication function), g" is S (the successor function), o" is < (the usual order relation) and c" is the number 0. (a) What is the interpretation of the term fi(g(g(c)), f2(g(x), y)) in N, where x" is 2 and y" is 3? Show your work. (b) Find the value of the A", where A is the L-formula (3x)(Vy)f2(x,y) = y. (c) Write an L-formula B(x) with a free variable x such that N = B(n) iff n is an odd nитber.
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