4. Consider again the structure R = (IR, +, x, <) and let P(x, y) be the predicate a < y. Express the predicate using a formula p(x, y) involving only + and x and not involving <. That is, find a formula p(x, y) such that P(x, y) and p(x, y) are logically equivalent in R with p(x, y) not involving the symbol <.
4. Consider again the structure R = (IR, +, x, <) and let P(x, y) be the predicate a < y. Express the predicate using a formula p(x, y) involving only + and x and not involving <. That is, find a formula p(x, y) such that P(x, y) and p(x, y) are logically equivalent in R with p(x, y) not involving the symbol <.
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
Related questions
Question
quesition4
![3. Consider the structure R =
(IR, +, ×, <). We say that a set C CR is definable in R if
there is a formula p(x) such that c E C if and only if p[c] is true in R. Show that the set
C = {0,1} is definable in R.
(Hint: Consider the polynomial whose solution is exactly 0 or 1.)
4. Consider again the structure R
(IR, +, ×, <) and let P(x, y) be the predicate x < y.
Express the predicate using a formula p(x, y) involving only + and × and not involving <.
That is, find a formula p(x, y) such that P(x, y) and p(x, y) are logically equivalent in R
with p(x, y) not involving the symbol <.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F02fb5ebf-5705-4258-b450-619941f18145%2F22683be9-421a-472c-9eef-a299abea7bf6%2Fj44tolr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Consider the structure R =
(IR, +, ×, <). We say that a set C CR is definable in R if
there is a formula p(x) such that c E C if and only if p[c] is true in R. Show that the set
C = {0,1} is definable in R.
(Hint: Consider the polynomial whose solution is exactly 0 or 1.)
4. Consider again the structure R
(IR, +, ×, <) and let P(x, y) be the predicate x < y.
Express the predicate using a formula p(x, y) involving only + and × and not involving <.
That is, find a formula p(x, y) such that P(x, y) and p(x, y) are logically equivalent in R
with p(x, y) not involving the symbol <.
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