1. **Problem Statement:** Design a light control system where a single light can be turned on or off from two different switches, such that toggling either switch changes the state of the light. 2. **Relevant Concept:** This is a classic example of a two-way switch circuit, which can be modeled logically using the XOR (exclusive OR) operation. 3. **Explanation:** - Let switch A and switch B be represented by binary variables $A$ and $B$, where $1$ means the switch is toggled (on) and $0$ means off. - The light's state $L$ depends on the XOR of $A$ and $B$: $$L = A \oplus B$$ - XOR outputs $1$ when inputs differ and $0$ when inputs are the same, which matches the behavior of the light toggling. 4. **Logical Equation and Circuit Implementation:** - The logical equation for the light control system is: $$L = A \oplus B = (A \land \neg B) \lor (\neg A \land B)$$ - This can be implemented using XOR gates or a combination of AND, OR, and NOT gates. 5. **Conclusion:** The light control system described can be implemented using an XOR gate, which matches the behavior of the two switches controlling one light. Final answer: $$L = A \oplus B$$