De Morgan_s Laws

De Morgan's Laws tell us how to negate Conjunctions and Disjunctions

For example, 'Miguel has a mobile phone and he has a laptop'

\begin{aligned} p & : = M i g u e l h a s a m o b i l e p h o n e \\ q & : = M i g u e l h a s a l a p t o p \end{aligned} $ $

\begin{align}
S &= p \land q \
\therefore \neg{S} &= \neg{(p \land q)} \
&\equiv \neg{p} \lor \neg{q}
\end

T h e r e f o r e, t h r o u g h t h e u s e o f D e M o r g a n^{'} s L a w s, w e k n o w n t h e n e g a t i o n o f t h e o r i g i n a l s t a t e m e n t i s : * * *^{'} M i g u e l d o e s n o t h a v e a m o b i l e o r h e d o e s n o t h a v e a l a p t o p^{'} * * *