https://file.aiquickdraw.com/mathbot/file/1726367207642ju7iajwp.jpg

The image you uploaded shows two logic circuits. Let's break them down step by step to identify their components and determine the Boolean expressions they represent.

### Top Circuit
- **Inputs:** `p` and `q`
- **Components:**
  - First, there is an OR gate that takes inputs `p` and `q` (output: \( p \lor q \)).
  - This output is connected to an AND gate as one of its inputs.
  - The other input to the AND gate is the negation of `q` (there is a NOT gate that inverts `q`).
  
  So, the output of the AND gate is:
  \[
  (p \lor q) \land \neg q
  \]

### Bottom Circuit
- **Inputs:** `p` and `q`
- **Components:**
  - First, there is an AND gate that takes inputs `p` and `q` (output: \( p \land q \)).
  - The output of this AND gate is passed to a NOT gate, giving \( \neg(p \land q) \).
  - This negated result is connected to an OR gate as one of its inputs.
  - The other input to the OR gate comes from an XOR gate, which takes inputs `p` and `q` (output: \( p \oplus q \)).
  
  So, the output of the OR gate is:
  \[
  \neg(p \land q) \lor (p \oplus q)
  \]

### Summary of Boolean Expressions:
1. **Top Circuit:** \((p \lor q) \land \neg q\)
2. **Bottom Circuit:** \(\neg(p \land q) \lor (p \oplus q)\)

Would you like further details or have any questions about the circuits? Here are some related questions to consider:

1. How does each gate work in a logic circuit (AND, OR, NOT, XOR)?
2. What truth tables correspond to these Boolean expressions?
3. How do De Morgan’s laws apply to simplify the expressions?
4. What real-world applications could these circuits have?
5. How would these circuits behave if `p` and `q` represent different binary inputs?

**Tip:** To fully understand logic circuits, it’s helpful to build their truth tables and study how the outputs change with different inputs.

What are the Boolean expressions of the logic circuits represented in the image?

Analyze the Boolean expressions represented by two different logic circuits. Understand the role of logic gates (AND, OR, NOT, XOR) and Boolean algebra in digital circuits, suitable for high school students in grades 9-12.

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