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.