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