I know De-Morgan's law that $$ -(p∧q) = -p∨-q $$ Also $$ -(p∨q) = -p∧-q $$ But for material implication and bi conditional operations there are also some transformation. What is the law or proof for it? Like $$ p⇒q = -p∨q $$ $$ p ↔q = (p∧q) ∨ (-p∧-q) $$ There may be other properties also that I don't know. How one can derive or say that? SideNote: Why PF don't have a negation ( tilda symbol) ?