Question:
Prove that: $ p \Rightarrow (q \Rightarrow r) \equiv (p \wedge q) \Rightarrow r $
Answer
We have:
$ \begin {array} {l}
p \Rightarrow \left ({q \Rightarrow r} \right) \equiv \bar p \vee \left ({q \Rightarrow r} \right) \\
\equiv \bar p \left ({\bar q \vee r} \right) \\< br> \equiv \left ({\bar p \vee \bar q} \right) \vee r \\\\equiv \overline {\left ({p \wedge q} \right)} \vee r \\
\equiv \left ({p \wedge q} \right) \Rightarrow r
\end { array} $