Questionnaire-2024/symbolic_encoding/1014.tex

\item \self Consider the following set operations and relations between
    two sets $X$ and $Y$, and an element $a$:
\begin{enumerate}
\item Union: $X \cup Y$
\item Intersection: $X \cap Y$
\item Set Difference: $X \setminus Y$
\item Containment: $a \in X$?
\item Subset: $X \subseteq Y$?
\item Strict Subset: $X \subset Y$?
\item Emptiness: $X=\emptyset$?
\item Equality: $X=Y$?
\end{enumerate}
Let $x$ and $y$ be the symbolic representations of $X$ and $Y$
respectively, and let $\alpha$ be the symbolic encoding of element
$a$. For each of the following items, state which of the above
operations is performed, or which of the above questions is answered.
Write the letters of the corresponding operation/question into the
boxes of the items below. Note that some of the items below do not
perform any of the above operations or answer any of the above
questions. Put a ``--'' in the box of these items. Also note that
some of the items below might do the same computation or answer the
same question.
\begin{itemize}
\item[\Huge{$\square$}] $\neg x \vee y$
\item[\Huge{$\square$}] $x \wedge y$
\item[\Huge{$\square$}] $x\equiv \top$?
\item[\Huge{$\square$}] $x\equiv y$?
\item[\Huge{$\square$}] $(x \rightarrow y) \wedge (y \rightarrow
    x)$?
\item[\Huge{$\square$}] $x\equiv \bot$?
\item[\Huge{$\square$}] $y \wedge \neg x$
\item[\Huge{$\square$}] $x \rightarrow \bot$?
\item[\Huge{$\square$}] $\alpha \models x$?
\item[\Huge{$\square$}] $\alpha \models \neg x$?
\item[\Huge{$\square$}] $\neg \alpha \models x$?
\item[\Huge{$\square$}] $x \rightarrow \alpha$?
\item[\Huge{$\square$}] $y \rightarrow x$?
\item[\Huge{$\square$}] $x \rightarrow y$?
\item[\Huge{$\square$}] $(x \rightarrow y) \wedge (x\not \equiv
    y)$?
\end{itemize}