Scenario: Imagine you are an engineer tasked with designing the logic for a smart home security system. The system involves various sensors and actuators to monitor and control different aspects of the home's security. Your goal is to use Boolean algebra and logic gates to create a logical framework that efficiently represents the conditions and actions for the smart home security system.

On the basis of the above scenario, answer the following questions.

Question $1$:

a$.$ Define Boolean expressions for the following conditions:

i$)$ Motion sensor in the living room is triggered.

ii$)$ The front door is opened.