$\backslash$section$*\{$Problem $2\}$

Use De Morgan's law for quantified statements and the laws of propositional logic to show the following equivalences:$\backslash \backslash$

$\backslash$begin$\{$enumerate$\}[$label$=(\backslash$alph$*)]$

$\backslash$item $

eg $\backslash$forall x $\backslash ,\backslash$left$($P$($x$)\backslash$land

eg Q$($x$)\backslash$right$)\backslash$; $\backslash$equiv $\backslash$; $\backslash$exists x $\backslash ,\backslash$left$($

eg P$($x$)\backslash$lor Q$($x$)\backslash$right$)$$$\backslash \backslash \backslash \backslash$

$\%$Enter your answer below this comment line.

$\backslash \backslash \backslash \backslash$

$\backslash$item $

eg $\backslash$forall x $\backslash ,\backslash$left$($

eg P$($x$)\backslash$to Q$($x$)\backslash$right$)\backslash$; $\backslash$equiv $\backslash$; $\backslash$exists x $\backslash ,\backslash$left$($

eg P$($x$)\backslash$land

eg Q$($x$)\backslash$right$)$$$\backslash \backslash \backslash \backslash$

$\%$Enter your answer below this comment line.

$\backslash \backslash \backslash \backslash$

$\backslash$item $

eg $\backslash$exists x $\backslash ,\backslash$big$($

eg P$($x$)\backslash$lor $\backslash$left$($Q$($x$)\backslash$land

eg R$($x$)\backslash$right$)\backslash$big$)\backslash$; $\backslash$equiv $\backslash$; $\backslash$forall x $\backslash ,\backslash$big$($ P$($x$)\backslash$land $\backslash$left$($

eg Q$($x$)\backslash$lor R$($x$)\backslash$right$)\backslash$big$)$$$\backslash \backslash \backslash \backslash$

$\%$Enter your answer below this comment line.

$\backslash \backslash \backslash \backslash$

$\backslash$end$\{$enumerate$\}$