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Draw the logical diagram to implement the following Boolean expression.

The image provided shows a set of Boolean expressions for which you need to draw the logical diagrams. Let me transcribe and explain each expression, then I'll describe how to construct the logic diagram for one of them.

### Transcription of Boolean Expressions:
1. **Expression 1**: \( F = \overline{(1 + X)} \cdot (\overline{Y} + Z) \)
2. **Expression 2**: \( F = (\overline{X} \cdot Y) \cdot \overline{Z} \)
3. **Expression 3**: \( F = \overline{[(\overline{X} \cdot \overline{Y}) + \overline{Z}] \cdot XY} \)
4. **Expression 4**: \( F = \overline{A + B} \cdot \overline{B + C} \)
5. **Expression 5**: \( F = \overline{(A + B + \overline{C})} \cdot (B \cdot \overline{A + C}) \)

### Constructing a Logic Diagram:
Let’s focus on **Expression 1**: \( F = \overline{(1 + X)} \cdot (\overline{Y} + Z) \)

#### Steps to Draw the Logic Diagram:
1. **Identify the Operators**:
   - \( 1 + X \) represents an OR gate.
   - \( \overline{(1 + X)} \) represents a NOT gate applied to the output of the OR gate.
   - \( \overline{Y} \) represents a NOT gate applied to input \( Y \).
   - \( \overline{Y} + Z \) represents an OR gate between the output of the NOT gate applied to \( Y \) and input \( Z \).
   - The final multiplication \( \overline{(1 + X)} \cdot (\overline{Y} + Z) \) represents an AND gate between the two intermediate results.

2. **Steps**:
   1. Use an OR gate to combine \( 1 \) and \( X \).
   2. Pass the result through a NOT gate to get \( \overline{(1 + X)} \).
   3. Use a NOT gate to invert \( Y \) to get \( \overline{Y} \).
   4. Use an OR gate to combine \( \overline{Y} \) and \( Z \).
   5. Finally, use an AND gate to combine the output of the NOT gate (from step 2) and the OR gate (from step 4).

This completes the logic diagram for the first expression. You can follow similar steps for the other expressions.

Would you like a detailed explanation or diagram for another specific Boolean expression? 

### Follow-up Questions:
1. Would you like the logic diagram for Expression 2 explained?
2. Are you interested in understanding how the NOT gate works in more complex expressions?
3. Would you like a step-by-step breakdown for the third Boolean expression?
4. Do you need assistance with any particular logic gate concepts?
5. Are you familiar with using De Morgan's laws in simplifying Boolean expressions?

### Tip:
When constructing logic diagrams, always start by identifying the basic gates (AND, OR, NOT) needed for each part of the expression before connecting them into a full circuit.

Learn how to implement Boolean expressions using logic diagrams. Understand Boolean algebra, logic gates, and De Morgan's laws through detailed examples and step-by-step diagrams.

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