1. The problem is to express the function $$F(A,B,C) = AB' C' + AC + (B + C')$$ using logic gates and draw its circuit diagram. 2. First, simplify the function if possible. 3. The function is $$F = AB' C' + AC + (B + C')$$. 4. Note that $$B + C'$$ is already a sum (OR) term. 5. The term $$AB' C'$$ means $$A \cdot B' \cdot C'$$ (AND of A, NOT B, and NOT C). 6. The term $$AC$$ means $$A \cdot C$$ (AND of A and C). 7. So the function is the OR of three terms: $$AB' C'$$, $$AC$$, and $$B + C'$$. 8. The term $$B + C'$$ is an OR gate with inputs B and NOT C. 9. To implement $$F$$, use: - NOT gates for $$B'$$ and $$C'$$. - AND gates for $$AB' C'$$ and $$AC$$. - OR gates to combine $$B$$ and $$C'$$, then to combine all three terms. 10. The circuit diagram steps: - Input variables: A, B, C. - Use NOT gates to get $$B'$$ and $$C'$$. - Use an AND gate with inputs A, $$B'$$, and $$C'$$ to get $$AB' C'$$. - Use an AND gate with inputs A and C to get $$AC$$. - Use an OR gate with inputs B and $$C'$$ to get $$B + C'$$. - Use a final OR gate to combine $$AB' C'$$, $$AC$$, and $$B + C'$$ to get $$F$$. Final answer: The function $$F(A,B,C) = AB' C' + AC + (B + C')$$ can be implemented using NOT gates for complements, AND gates for products, and OR gates for sums as described above.