dæ Vy (E(x,y) → B(x) ^ W (y))
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
![**Logical Expression Translation**
Let \( B(x) \) mean \( x \) is a bird, let \( W(x) \) mean \( x \) is a worm, and let \( E(x, y) \) mean \( x \) eats \( y \). Find an English sentence to describe the following expression:
\[
\forall x \, \forall y \, (E(x, y) \rightarrow B(x) \land W(y))
\]
**Explanation:**
The expression uses logical quantifiers and connectors to describe a relationship between elements \( x \) and \( y \).
- \(\forall x\) indicates "for every \( x \)".
- \(\forall y\) indicates "for every \( y \)".
- \(E(x, y) \rightarrow B(x) \land W(y)\) states that if \( x \) eats \( y \), then \( x \) must be a bird and \( y \) must be a worm.
**English Translation:**
For every entity \( x \) and every entity \( y \), if \( x \) eats \( y \), then \( x \) is a bird and \( y \) is a worm.
This logical expression is essentially defining that within the given system, only birds eat worms.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74d35d78-10f2-4c7e-8a1f-3d0300cedc60%2Faf53272e-8e3e-4147-bb12-af464f0538b2%2F5db112j_processed.png&w=3840&q=75)
Transcribed Image Text:**Logical Expression Translation**
Let \( B(x) \) mean \( x \) is a bird, let \( W(x) \) mean \( x \) is a worm, and let \( E(x, y) \) mean \( x \) eats \( y \). Find an English sentence to describe the following expression:
\[
\forall x \, \forall y \, (E(x, y) \rightarrow B(x) \land W(y))
\]
**Explanation:**
The expression uses logical quantifiers and connectors to describe a relationship between elements \( x \) and \( y \).
- \(\forall x\) indicates "for every \( x \)".
- \(\forall y\) indicates "for every \( y \)".
- \(E(x, y) \rightarrow B(x) \land W(y)\) states that if \( x \) eats \( y \), then \( x \) must be a bird and \( y \) must be a worm.
**English Translation:**
For every entity \( x \) and every entity \( y \), if \( x \) eats \( y \), then \( x \) is a bird and \( y \) is a worm.
This logical expression is essentially defining that within the given system, only birds eat worms.
Expert Solution
Step 1
Given,
| B(x) | x is a bird |
| W(x) | x is a worm |
| E(x, y) | x eats y |
The different symbols are used:
is a universal quantifier.
is only if
is AND predicate
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