1. The problem is to write the logic diagram for the function $F_1 = (A + B + C) + (AB') + (BC)$. 2. The formula uses OR ($+$) and AND (juxtaposition) operations, and NOT (') for complements. 3. Break down each term: - $A + B + C$ is an OR gate with inputs A, B, C. - $AB'$ is an AND gate with inputs A and NOT B. - $BC$ is an AND gate with inputs B and C. 4. Then, these three outputs are ORed together. 5. The logic diagram consists of: - One OR gate with inputs A, B, C. - One NOT gate for B, feeding into an AND gate with A. - One AND gate with inputs B and C. - One OR gate combining the outputs of the above three gates. 6. This completes the logic diagram for the first function. Since the user requested only the first problem solved, the rest are ignored as per instructions.