Example: Applying logical equivalences to derive a new equivalence
Without using truth tables, show that ?[p?(?p?q)] ? ?p??q
?[p?(?p?q)] ? ?p ? ?(?p?q) from the second De Morgan’s law
? ?p ? [?(?p) ? ?q] from the first De Morgan’s law
? ?p ? (p??q) from the double negation law
? (?p?p) ? (?p??q) from the distributive law
? F ? (?p??q) since ?p?p ? F
? (?p??q) ? F from the commutative law for ?
? ?p??q from the identity law for F