1. The problem asks to state the Boolean expression laws. 2. Boolean algebra has several fundamental laws that govern the operations AND ($\cdot$), OR ($+$), and NOT ($\overline{\cdot}$). These laws allow simplification and manipulation of Boolean expressions. 3. Some key Boolean laws include: - **Identity Law**: $A + 0 = A$ and $A \cdot 1 = A$ - **Null Law**: $A + 1 = 1$ and $A \cdot 0 = 0$ - **Idempotent Law**: $A + A = A$ and $A \cdot A = A$ - **Complement Law**: $A + \overline{A} = 1$ and $A \cdot \overline{A} = 0$ - **Commutative Law**: $A + B = B + A$ and $A \cdot B = B \cdot A$ - **Associative Law**: $(A + B) + C = A + (B + C)$ and $(A \cdot B) \cdot C = A \cdot (B \cdot C)$ - **Distributive Law**: $A \cdot (B + C) = (A \cdot B) + (A \cdot C)$ and $A + (B \cdot C) = (A + B) \cdot (A + C)$ - **De Morgan's Laws**: $\overline{A \cdot B} = \overline{A} + \overline{B}$ and $\overline{A + B} = \overline{A} \cdot \overline{B}$ 4. These laws are essential to simplify and analyze Boolean expressions effectively.