1. Consider the formula A = (vx ₁(x, a₁)) → (y (p2(y) ^ P3(y, α2))). (a) Create a formula tree for A. (b) Give two examples of interpretations for A. (c) Determine the truth value of A under the interpretation 9 = (Z, {≥, prime(), <}, {0,2}), where prime() is the relation that determines whether its argument is a prime number, i.e. the relation prime(r) is satisfied if and only if r is prime.
1. Consider the formula A = (vx ₁(x, a₁)) → (y (p2(y) ^ P3(y, α2))). (a) Create a formula tree for A. (b) Give two examples of interpretations for A. (c) Determine the truth value of A under the interpretation 9 = (Z, {≥, prime(), <}, {0,2}), where prime() is the relation that determines whether its argument is a prime number, i.e. the relation prime(r) is satisfied if and only if r is prime.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Consider the formula
A = (vx ₁(x, ₁)) → (y (p2(y) ^ P3(y, α2))).
(a) Create a formula tree for A.
(b) Give two examples of interpretations for A.
(c) Determine the truth value of A under the interpretation
9 = (Z, {≥, prime(), <}, {0,2}),
where prime() is the relation that determines whether its argument is a prime number,
i.e. the relation prime(r) is satisfied if and only if r is prime.
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