The Boolean expression ∼(p∨q)∨(∼p∧q) is simplified as follows: Start with the given expression: ∼(p∨q)∨(∼p∧q) Apply De Morgan's Law: (∼p∧∼q)∨(∼p∧q) Use the Distributive Law: ∼p∧(∼q∨q) By the Complement Law, ( ∼q∨q ) is a tautology (t) : ∼p∧t Finally, apply the Identity Law: ∼p Therefore, the expression simplifies to ∼p.