1. **State the problem:** Simplify the Boolean expression $$F = AB\overline{B} + AC(AB)$$ and understand its logic gate representation. 2. **Recall Boolean algebra rules:** - $$B\overline{B} = 0$$ because a variable AND its complement is always 0. - $$AB$$ means $$A \land B$$. - Multiplication represents AND, addition represents OR. 3. **Simplify the expression step-by-step:** - Start with $$F = AB\overline{B} + AC(AB)$$ - Since $$B\overline{B} = 0$$, then $$AB\overline{B} = A \cdot 0 = 0$$ - So, $$F = 0 + AC(AB) = AC(AB)$$ - Note that $$AC(AB) = A C A B = A A B C = A B C$$ (because $$A \cdot A = A$$) 4. **Final simplified expression:** $$F = ABC$$ 5. **Interpretation:** - The output $$F$$ is true only when $$A$$, $$B$$, and $$C$$ are all true. 6. **Logic gate description:** - The simplified circuit is a single AND gate with inputs $$A$$, $$B$$, and $$C$$. **Answer:** $$F = ABC$$