1. Problem: Simplify the Boolean expression $$Y = AB + \overline{A}C + BC$$. 2. Formula and rules: Use Boolean algebra simplification rules such as the Distributive Law, Consensus Theorem, and Absorption Law. 3. Work: - Original expression: $$Y = AB + \overline{A}C + BC$$ - Apply Consensus Theorem: $$AB + \overline{A}C + BC = AB + \overline{A}C$$ (since $$BC$$ is redundant) - Factor: $$Y = AB + \overline{A}C$$ 4. Explanation: The term $$BC$$ is covered by the other terms, so it can be removed. 5. Final answer: $$Y = AB + \overline{A}C$$