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minor tweaks in first two chapters

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Lauchmelder 2021-12-05 19:20:22 +01:00
parent 2d333df67a
commit 43d97281b6
3 changed files with 14746 additions and 14695 deletions
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chapters/sections/logic.tex
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@ -5,7 +5,7 @@
\begin{document}
\section{Logic}
\begin{defi}[Statements]
A statement is a sentence (mathematically or colloquially) which can be either true or false.
A statement is a sentence (mathematical or colloquial) which can be either true or false.
\end{defi}
\begin{eg}
@ -54,7 +54,7 @@ are also statements. We can represent connectives with truth tables
\end{rem}
\begin{defi}[Hierarchy of logical operators]
$\neg$ is stronger than $\wedge$ and $\vee$, which are stronger than $\implies$ and $\iff$.
$\neg$ binds stronger than $\wedge$ and $\vee$, which bind stronger than $\implies$ and $\iff$.
\end{defi}
\begin{eg}\leavevmode
@ -88,7 +88,7 @@ Let $\Phi(x)$ be a statement depending on $x$. Then $\forall x ~\Phi(x)$ and $\e
\item If the domain is infinite the truth value of $\forall x ~\Phi(x)$ cannot be algorithmically determined.
\item $\forall x ~\Phi(x)$ and $\forall y ~\Phi(y)$ are equivalent.
\item Same operators can be exchanged, different ones cannot.
\item $\forall x ~\Phi(x)$ is equivalent to $\neg\exists x ~\neg\Phi(x)$.
\item $\forall x ~\Phi(x)$ is equivalent to $\neg(\exists x ~\neg\Phi(x))$.
\end{enumerate}
\end{rem}