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\title {Logic I \\ Lecture 14}

\maketitle

# Lecture 14

\def \ititle {Logic I}
\def \isubtitle {Lecture 14}
\begin{center}
{\Large
\textbf{\ititle}: \isubtitle
}

\iemail %
\end{center}
Readings refer to sections of the course textbook, \emph{Language, Proof and Logic}.

\section{Two Things Are Broken}

\section{Two Things Are Broken}
To translate sentences involving number into awFOL, use identity. For example,
`Two things are broken' might be translated as:
∃x ∃y ( Broken(x) ∧ Broken(y) ∧ ¬(x=y) )

## Loving and Being Loved

\section{Loving and Being Loved}

\section{Loving and Being Loved}

#

## Quantifier Equivalences: ∀x(Square(x) → Broken(x)) ⫤⊨ ∀x(¬Broken(x) → ¬Square(x))

\section{Quantifier Equivalences: ∀x(Square(x) → Broken(x)) ⫤⊨ ∀x(¬Broken(x) → ¬Square(x))}

\section{Quantifier Equivalences: ∀x(Square(x) → Broken(x)) ⫤⊨ ∀x(¬Broken(x) → ¬Square(x))}
10.20, 10.22

\section{Quantifier Equivalences: ∀x(Square(x) → Broken(x)) ⫤⊨ ∀x(¬Square(x) ∨ Broken(x))}