The domain of {\bf discourse} for this problem is a group of three people who are working on a project. To make notation easier, the people are numbered $1, \; 2, \; 3$. The predicate $M (x,\; y)$ indicates whether x has sent an email to Sy$, so $M(2, \;3)$ is read below shows the value of the predicate $M(x,\;y)$ for each $(x,\;y)$ pair. The truth value in row $x$ and column $y$ gives the truth value for $M (x , \; y) $. \\|\ Person $2$ has sent an email to person $3$.'' The table \begin{array}{||c||c|c|c||} \hline\hline M & 1 & 2& 3\\ \hline\hline 1 &T & T & T\\ \hline 2 &T & F & T\\ \hline 3 &T & T & F\\ \hline\hline \end{array} \]\\\\ {\bf Determine if the quantified statement is true or false. Justify your answer.}\\ \begin{enumerate}[label=(\alph*)] \item $\forall x \, \forall y \left(x\not= y)\;\to \; M(x,\;y)\right)$\\\\ %Enter your answer below this comment line. \\\\ \item $\foral1 x \, \exists y \;\; \neg M(x,\;y)$\\\\ %Enter your answer below this comment line. \\\\ \item $\exists x \, \foral1 y \;\; m(x,\;y)$\\\\ %Enter your answer below this comment line. \\\\ \end{enumerate}

The domain of {\bf discourse} for this problem is a group of three people who are working on a project. To make notation easier, the people are numbered $1, \; 2, \; 3$. The predicate $M (x,\; y)$ indicates whether x has sent an email to Sy$, so $M(2, \;3)$ is read below shows the value of the predicate $M(x,\;y)$ for each $(x,\;y)$ pair. The truth value in row $x$ and column $y$ gives the truth value for $M (x , \; y) $. \\|\ Person $2$ has sent an email to person $3$.'' The table \begin{array}{||c||c|c|c||} \hline\hline M & 1 & 2& 3\\ \hline\hline 1 &T & T & T\\ \hline 2 &T & F & T\\ \hline 3 &T & T & F\\ \hline\hline \end{array} \]\\\\ {\bf Determine if the quantified statement is true or false. Justify your answer.}\\ \begin{enumerate}[label=(\alph*)] \item $\forall x \, \forall y \left(x\not= y)\;\to \; M(x,\;y)\right)$\\\\ %Enter your answer below this comment line. \\\\ \item $\foral1 x \, \exists y \;\; \neg M(x,\;y)$\\\\ %Enter your answer below this comment line. \\\\ \item $\exists x \, \foral1 y \;\; m(x,\;y)$\\\\ %Enter your answer below this comment line. \\\\ \end{enumerate}

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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