finding CNF and a logically Logically equivalent DNF for Propositional form (p→(q→r))

Question

I can write the truth table for (p→(q→r)) but i was not able to find the required CNF and a logically Logically equivalent DNF for Propositional form (p→(q→r)) . It's confusing.

Answer 1

Since $A\rightarrow B$ is defined as $\lnot A\lor B$, we can write $(1)$ as $(2)$.

\begin{equation}\tag{1} (p\rightarrow(q\rightarrow r)) \end{equation} \begin{equation}\tag{2} (\lnot p)\lor(\lnot q)\lor r \end{equation}

Formula $(2)$ is in disjunctive normal form already, since logical OR is the major connective. Note that we can also form the conjunction of $(2)$ with logical true (denoted here as $1$), which makes a CNF formula.

\begin{equation}\tag{3} \big((\lnot p)\lor(\lnot q)\lor r\big)\land 1 \end{equation}

It is common to refer $(2)$ as a CNF expression with 1 conjunct.