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## Translation with Quantifiers

\begin{minipage}{\columnwidth}
All discordians weep:
∀x( Dscrdn(x) → Wps(x) )
\end{minipage}
\begin{minipage}{\columnwidth}
∀x( ( \textbf{Quadr(x) ∧} Dscrdn(x) ) → Wps(x) )
\end{minipage}
\begin{minipage}{\columnwidth}
All quadrumanous discordians weep \textbf{and wail}:
∀x( ( Quadr(x) ∧ Dscrdn(x) ) → ( Wps(x) \textbf{ ∧ Wls(x)} ) )
\end{minipage}
\begin{minipage}{\columnwidth}
All quadrumanous discordians weep and wail \textbf{except Gillian Deleude}:
∀x( ( Quadr(x) ∧ Dscrdn(x) \textbf{∧ ¬(x=a)} ) → ( Wps(x) ∧ Wls(x) ) )
\end{minipage}

Some persuasive and useful arguments are not valid.

∃x(Persuasive(x) Useful(x) Argument(x) ∧ ¬Valid(x))

All discordians weep.

∀x( Dscrdn(x) Wps(x) )

∀x( (Quadr(x)∧ Dscrdn(x) ) → Wps(x) )

All quadrumanous discordians weep and wail.

∀x( ( Quadr(x) ∧ Dscrdn(x) ) → ( Wps(x) ∧ Wls(x) ) )

All quadrumanous discordians weep and wail except Gillian Deleude.

∀x( ( Quadr(x) ∧ Dscrdn(x) ∧ ¬(x=a) ) → ( Wps(x) ∧ Wls(x) ) )

9.4–-9.5
9.8–-9.9
9.12-–9.13