1. Consider the formula A = (Vx pi(x, a1)) → (3y (p2(y) p3(y, a2)) ^ (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 x is prime.
1. Consider the formula A = (Vx pi(x, a1)) → (3y (p2(y) p3(y, a2)) ^ (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 x is prime.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4575c695-56bc-4a6a-843f-ec886ca258f2%2F95ee5f6a-25eb-46e3-a260-f1cd6d4c54e7%2F1qnvzn_processed.jpeg&w=3840&q=75)
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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