**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.

Given, B(x) x is a bird W(x) x is a worm E(x, y) x eats y The different symbols are…

Answered: dæ Vy (E(x,y) → B(x) ^ W (y))

Engineering

Computer Science

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

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Concept explainers

Representation of Polynomial

It is necessary for the polynomial expression that each expression consists of two parts:

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.

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:

$\forall$ is a universal quantifier.

$\to$ is only if

$\land$ is AND predicate

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