Disjunctive Normal Form I need some help understanding how to convert a formula into disjunctive normal form. Can anybody explain how one would write φ = ((p ∨ q ∨ r) → (¬p ∧ r)) in disjunctive normal form? Is it possible to use truth tables to help converting to DNF form?

I think a truth table could work for simpler propositions, but this one in question is relatively complicated - using logical equivalences might be easier.

Consider a conditional proposition $P \implies Q$, this is equivalent to $(\
eg P \vee Q)$, which can be verified using a truth table.

Thus considering, $\varphi = ((P \vee Q \vee R) \implies (\
eg P \land R))$, \begin{align} &\phantom{{}\equiv{}} ((P \vee Q \vee R) \implies (\
eg P \land R))\\\ &\equiv \
eg (P \vee Q \vee R) \vee (\
eg P \land R) \\\ &\equiv ((\
eg P) \land (\
eg Q) \land (\
eg R)) \vee (\
eg P \land R) \\\ &\equiv ((\
eg P \land R) \vee \
eg P) \land ((\
eg P \land R) \vee \
eg Q) \land ((\
eg P \land R) \vee \
eg R) \\\ & \phantom{((P \vee Q \vee R) \implies} \vdots \end{align} which can be simplified using logical equivalences.

Hope this helps.