Translate each of these nested quantifications into an English statement that expresses a mathematical fact. The domain in each case consists of all real numbers. a) ∃x∀y(x + y = y) b) ∀x∀y (((x ≥ 0) ∧ (y < 0)) → (x − y > 0)) c) ∃x∃y(((x ≤ 0) ∧ (y ≤ 0)) ∧ (x − y > 0)) d) ∀x∀y((x ≠ 0) ∧ (y ≠ 0) ↔ (xy ≠ 0))
Translate each of these nested quantifications into an English statement that expresses a mathematical fact. The domain in each case consists of all real numbers. a) ∃x∀y(x + y = y) b) ∀x∀y (((x ≥ 0) ∧ (y < 0)) → (x − y > 0)) c) ∃x∃y(((x ≤ 0) ∧ (y ≤ 0)) ∧ (x − y > 0)) d) ∀x∀y((x ≠ 0) ∧ (y ≠ 0) ↔ (xy ≠ 0))
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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Translate each of these nested quantifications into an English statement that expresses a mathematical
fact. The domain in each case consists of all real numbers.
a) ∃x∀y(x + y = y)
b) ∀x∀y (((x ≥ 0) ∧ (y < 0)) → (x − y > 0))
c) ∃x∃y(((x ≤ 0) ∧ (y ≤ 0)) ∧ (x − y > 0))
d) ∀x∀y((x ≠ 0) ∧ (y ≠ 0) ↔ (xy ≠ 0))
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