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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![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}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4dfe21d-8841-4a7f-87f3-5b1d44dd027a%2F98376236-5f08-4a5f-94ce-425bd76f7bf7%2Fqu12swj.png&w=3840&q=75)
Transcribed Image Text: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}
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