Question

The expression \( a = \overline{AB} \) is equal to:

• A. \( \overline{A} + \overline{B} \)
• B. \( AB + A \)
• C. \( A + B \)
• D. \( AB \)

Hint:

De Morgan: \( \overline{AB} = \overline{A} + \overline{B},\quad \overline{A + B} = \overline{A} \cdot \overline{B} \)

Answer 1

The Correct Option is A

To solve this problem, we need to simplify the Boolean expression \( a = AB \).

1. Understanding the Boolean Expression: 

- The given Boolean expression is \( a = AB \), where \( A \) and \( B \) are Boolean variables. 
We need to determine the simplified or equivalent form of this expression.

2. Simplification Process:

- The expression \( a = AB \) is already in its simplest form. There is no need for further simplification because it represents the AND operation between \( A \) and \( B \).

3. Final Simplified Expression:

- The expression \( AB \) is already in the minimal sum of products form, and it cannot be simplified any further.

4. Final Answer:

The expression \( a = AB \) is already in its simplest form, and there is no further simplification needed. The equivalent expression is \( AB \).