Algebra of Propositional Logic How can I rewrite the following propositions in their simplest equivalent forms 
i.e. Least atomic propositions


*

*$(p \land \neg p) \Rightarrow \neg p$

*$\neg ((p \land\neg p) \Rightarrow \neg q) $

*$\neg ((p \land q) \Rightarrow r)$
Thanks

The third one can be simplified to $p \land q \land \neg r$:
$$\neg (( p \land q) \rightarrow r) \Leftrightarrow \text{ (Implication)}$$
$$\neg (\neg (p \land q) \lor r) \Leftrightarrow \text{ (DeMorgan)}$$
$$\neg \neg (p \land q) \land \neg r \Leftrightarrow \text{ (Double Negation)}$$
$$(p \land q) \land \neg r \Leftrightarrow \text{ (Association)}$$
$$p \land q \land \neg r$$
