(4) 4. Let P(x,y)= "x sent a text message to y." The u.d. for both x and y is all people. Translate into symbols: a. Everyone has sent a text message to someone. b. Everyone has been sent a text message by someone.

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
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### Problem 4: Translation of Statements into Symbols

Let \( P(x, y) \) denote "x sent a text message to y." The universe of discourse (u.d.) for both \( x \) and \( y \) is all people. Translate the following statements into symbolic form:

**a. Everyone has sent a text message to someone.**

Translated Symbolically: 
\[ \forall x \, \exists y \, P(x, y) \]
This can be read as: "For every person \( x \), there exists a person \( y \) such that \( x \) sent a text message to \( y \)."

**b. Everyone has been sent a text message by someone.**

Translated Symbolically:
\[ \forall x \, \exists y \, P(y, x) \]
This can be read as: "For every person \( x \), there exists a person \( y \) such that \( y \) sent a text message to \( x \)."
Transcribed Image Text:### Problem 4: Translation of Statements into Symbols Let \( P(x, y) \) denote "x sent a text message to y." The universe of discourse (u.d.) for both \( x \) and \( y \) is all people. Translate the following statements into symbolic form: **a. Everyone has sent a text message to someone.** Translated Symbolically: \[ \forall x \, \exists y \, P(x, y) \] This can be read as: "For every person \( x \), there exists a person \( y \) such that \( x \) sent a text message to \( y \)." **b. Everyone has been sent a text message by someone.** Translated Symbolically: \[ \forall x \, \exists y \, P(y, x) \] This can be read as: "For every person \( x \), there exists a person \( y \) such that \( y \) sent a text message to \( x \)."
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