To determine the correct logical equation for the logic circuit in Figure 3, we need to analyze the circuit's components and how they interact. Since we don't have the visual representation of the circuit, I will guide you through the logical reasoning process that you would typically follow when analyzing a logic circuit. Step-by-Step Explanation

1. Identify the Components:
2. In a logic circuit, the basic components are logic gates such as AND, OR, and NOT gates. Each gate has a specific function:
   • AND Gate: Outputs true (1) only if all its inputs are true (1).
   • OR Gate: Outputs true (1) if at least one of its inputs is true (1).
   • NOT Gate: Outputs the opposite of its input (inverts the input).
3. Analyze the Circuit:
4. Without the figure, let's assume a common configuration. For example, if the circuit has two inputs A and B going into an AND gate, and the output of this AND gate is then combined with another input C through an OR gate, the output would be represented as:
   • ( Z = A \cdot B + C )
5. This corresponds to option B: ( Z = A \cdot B + C ).
6. Evaluate Each Option:
7. Option A: ( \overline{A} + B \cdot \overline{C} ): This suggests that the output is true if A is false or if both B is true and C is false. This does not match our assumed configuration.
8. Option B: ( Z = A \cdot B + C ): This indicates that the output is true if both A and B are true, or if C is true. This is a common output for circuits with an AND gate followed by an OR gate, making it a strong candidate.
9. Option C: ( Z = A + B \cdot C ): This suggests that the output is true if A is true or if both B and C are true. This does not match our assumed configuration.
10. Option D: ( Z = \overline{A} \cdot B + \overline{C} ): This indicates that the output is true if A is false and B is true, or if C is false. This also does not match our assumed configuration.
11. Conclusion:
12. Based on the analysis, option B is the most logical representation of a common circuit configuration involving an AND gate followed by an OR gate. Therefore, the correct answer is B: ( Z = A \cdot B + C ).

Summary of Why Other Options Are Incorrect:

• Option A: Incorrect because it does not represent a typical combination of AND and OR gates.
• Option C: Incorrect as it suggests a different logical relationship that does not match the assumed circuit.
• Option D: Incorrect because it implies a different condition for the output that does not align with standard logic gate configurations.

Revision Summary:

• Understand the functions of basic logic gates: AND, OR, and NOT.
• Analyze the circuit step-by-step, identifying how inputs are combined.
• Evaluate each option against the logical structure of the circuit.
• Recognize that common configurations often lead to specific logical equations.

By following these steps, you can effectively analyze logic circuits and determine the correct logical equations associated with them.