https://file.aiquickdraw.com/mathbot/file/17271029049707cf14yoj.jpg

Let's analyze the Boolean expressions for both circuits in the image provided.

### (a) Gambar 9.25:

The circuit shows three switches \( x \), \( y \), and \( z' \). We have:
- Switch \( x \) and \( y \) are in parallel, meaning the Boolean expression for this part is \( x + y \) (logical OR, representing either switch being ON allows current to pass).
- Then, the result of \( x + y \) is in series with \( z' \) (complement of \( z \)), meaning the Boolean expression for the whole circuit is:
\[
(x + y) \cdot z'
\]
(Logical AND, indicating that both must be ON for current to pass to B).

### (b) Gambar 9.26:

This circuit involves three switches \( x \), \( y \), and \( z \) in parallel, and another path with \( x \) and \( z' \) in series. We can describe this as:
- The first part, with \( x \), \( y \), and \( z \) in parallel, is expressed as \( x + y + z \).
- The second path is \( x \) and \( z' \) in series, expressed as \( x \cdot z' \).
- These two parts are then in parallel, so the final Boolean expression is:
\[
(x + y + z) + (x \cdot z')
\]
(Logical OR of the two parallel paths).

### Final Boolean Expressions:
- For (a): \((x + y) \cdot z'\)
- For (b): \((x + y + z) + (x \cdot z')\)

Let me know if you need further clarification or details!

### Related Questions:
1. What is the difference between series and parallel circuits in Boolean logic?
2. How do you simplify Boolean expressions using Karnaugh maps?
3. Can De Morgan's law be applied to simplify the Boolean expressions in the given circuits?
4. How would you convert a Boolean expression into a logic gate diagram?
5. What are the practical uses of Boolean algebra in designing electrical circuits?

### Tip:
When working with Boolean expressions, remember to follow the correct order of operations: complement (NOT), AND, and then OR, similar to how arithmetic operations are structured.

Tentukan ekspresi-ekspresi Boole yang mendeskripsikan sistem saklar (Gambar 25 dan 26) berikut.

Solve the Boolean expressions for series and parallel circuits as shown in Gambar 9.25 and Gambar 9.26. Learn how to derive the Boolean formulas using Boolean algebra and logic gates for circuits involving switches x, y, z, and their complements.

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