Boolean algebra：練習問題

Which Boolean identity is represented by the expression \( A \cdot (B + C) = A \cdot B + A \cdot C \)?

Simplify the Boolean expression: \( (A + B) \cdot (A + \overline{B}) \).

Simplify the following Boolean expression to its simplest form: \( \overline{\overline{A} + \overline{B}} + (A \cdot \overline{B}) \)

Simplify the Boolean expression: \( A + (A \cdot B) \).

Which Boolean expression is equivalent to the XOR operation \( A \oplus B \)?

In Boolean algebra, what is the value of the identity expression \( A + 0 \)?

What is the Boolean result of the expression \( A \cdot (\overline{A} + B) \) after simplification?

Simplify the expression \( (A + B) \cdot (A + \overline{B}) \) to its simplest form.

Using Boolean identities and De Morgan's laws, simplify the following expression to its simplest possible form:
\(Q = \overline{\overline{A \cdot B} + \overline{A \cdot C}}\)
Show each step of your simplification.

Prove using a truth table or Boolean algebraic identities that the following expression is a tautology (always true):
\(P = (A \cdot B) + (A \cdot \overline{B}) + \overline{A}\)