Let p and q be two statements, then q↔(~p∨~q)is logically equivalent to

q↔(~p∨~q) ≡q↔∼(p∧q)≡[q→∼(p∧q)]∧[~(p∧q)→q]≡[~q∨~(p∧q)]∧[(p∧q)∨q]≡∼[q∧(p∧q)]∧q≡∼(p∧q)∧q≡(~p∨~q)∧q≡(~p∧q)∨(~q∧q)≡(~p∧q)