Here are the solutions to the given expressions using Boolean algebra:

a) $1 \cdot \overline{0}$

• $\overline{0} = 1$
• So, $1 \cdot 1 = 1$

Answer: $1$

b) $1 + \overline{1}$

• $\overline{1} = 0$
• So, $1 + 0 = 1$

Answer: $1$

c) $\overline{0} \cdot 0$

• $\overline{0} = 1$
• So, $1 \cdot 0 = 0$

Answer: $0$

d) $\overline{(1 + 0)}$

• $1 + 0 = 1$
• So, $\overline{1} = 0$

Answer: $0$

Let me know if you'd like further details or have any questions!

Here are 5 related questions:

1. What is $\overline{1 + 1}$ in Boolean algebra?
2. Simplify $(1 \cdot 1) + \overline{0 \cdot 1}$.
3. Find the value of $0 + \overline{(0 \cdot 1)}$.
4. What is the result of $\overline{1 \cdot 0} + 1$?
5. Solve $(0 + \overline{1}) \cdot (1 + 0)$.

Tip: In Boolean algebra, the complement of 1 is 0 and the complement of 0 is 1.