(a) Create combinational circuit based on the following Boolean Expression. i) \( \left(x_{1} \cup \sim x_{2}\right)^{\prime} \cap x_{3} \), ii) \( \sim x_{1} \cap\left(x_{2} \cup x_{3}\right) \).

To create a combinational circuit based on the Boolean expressions provided, we can first break down each expression to understand the logic gates required. For the first expression \( \left(x_{1} \cup \sim x_{2}\right)^{\prime} \cap x_{3} \): 1. Begin with \( x_2 \) and apply a NOT gate to get \( \sim x_{2} \). 2. Then, use an OR gate to combine \( x_{1} \) and \( \sim x_{2} \). 3. Finally, apply a NOT gate to the output of the OR gate to find \( \left(x_{1} \cup \sim x_{2}\right)^{\prime} \) and AND it with \( x_{3} \) using an AND gate. For the second expression \( \sim x_{1} \cap\left(x_{2} \cup x_{3}\right) \): 1. Use a NOT gate on \( x_{1} \) to get \( \sim x_{1} \). 2. Use an OR gate to combine \( x_{2} \) and \( x_{3} \). 3. Finally, use an AND gate to combine the output of the NOT gate and the OR gate. With these components, you can design the corresponding combinational circuits. In creating these circuits, it helps to visualize the inputs, outputs, and the flow of signals through the gates, leading to the final outputs based on the given Boolean functions.