Exercise logic.propositional.dnf
Description
Proposition to DNF
Derivation
T /\ T /\ ((q /\ ~~(~~(~~q || p) /\ ~q)) || (~~~~~r /\ ~~(~~(~~q || p) /\ ~q))) /\ T
⇒ logic.propositional.idempandT /\ ((q /\ ~~(~~(~~q || p) /\ ~q)) || (~~~~~r /\ ~~(~~(~~q || p) /\ ~q))) /\ T
⇒ logic.propositional.truezeroand((q /\ ~~(~~(~~q || p) /\ ~q)) || (~~~~~r /\ ~~(~~(~~q || p) /\ ~q))) /\ T
⇒ logic.propositional.truezeroand(q /\ ~~(~~(~~q || p) /\ ~q)) || (~~~~~r /\ ~~(~~(~~q || p) /\ ~q))
⇒ logic.propositional.notnot(q /\ ~~(~~q || p) /\ ~q) || (~~~~~r /\ ~~(~~(~~q || p) /\ ~q))
⇒ logic.propositional.notnot(q /\ (~~q || p) /\ ~q) || (~~~~~r /\ ~~(~~(~~q || p) /\ ~q))
⇒ logic.propositional.notnot(q /\ (q || p) /\ ~q) || (~~~~~r /\ ~~(~~(~~q || p) /\ ~q))
⇒ logic.propositional.absorpand(q /\ ~q) || (~~~~~r /\ ~~(~~(~~q || p) /\ ~q))
⇒ logic.propositional.complandF || (~~~~~r /\ ~~(~~(~~q || p) /\ ~q))
⇒ logic.propositional.falsezeroor~~~~~r /\ ~~(~~(~~q || p) /\ ~q)
⇒ logic.propositional.notnot~~~r /\ ~~(~~(~~q || p) /\ ~q)
⇒ logic.propositional.notnot~r /\ ~~(~~(~~q || p) /\ ~q)
⇒ logic.propositional.notnot~r /\ ~~(~~q || p) /\ ~q
⇒ logic.propositional.notnot~r /\ (~~q || p) /\ ~q
⇒ logic.propositional.notnot~r /\ (q || p) /\ ~q
⇒ logic.propositional.andoveror~r /\ ((q /\ ~q) || (p /\ ~q))
⇒ logic.propositional.compland~r /\ (F || (p /\ ~q))
⇒ logic.propositional.falsezeroor~r /\ p /\ ~q