Question

The Boolean expressions \[ (AB)' = A' + B' \] and \[ (A+B)' = A'B' \] represent

• A. Absorption law
• B. Distributive law
• C. De Morgan's law
• D. Idempotent law

Hint:

Remember De Morgan's Laws: \[ (AB)'=A'+B' \] and \[ (A+B)'=A'B'. \] A useful memory trick is: When the complement enters the bracket, the operation changes from AND to OR or from OR to AND.

Answer 1

The Correct Option is C

Concept: Boolean Algebra is a mathematical system used extensively in digital electronics, switching circuits, computer science, and logic design. Among the most important laws of Boolean Algebra are De Morgan's Laws, which provide a relationship between complementation, addition (OR operation), and multiplication (AND operation). These laws are: \[ (AB)'=A'+B' \] and \[ (A+B)'=A'B'. \] These identities allow a complemented product to be expressed as a sum of complements and a complemented sum to be expressed as a product of complements.

Step 1: Examine the first Boolean expression. The first expression is \[ (AB)'=A'+B'. \] This states that the complement of the AND operation equals the OR operation of the individual complements. In words, \[ \text{NOT}(A \text{ AND } B) = (\text{NOT }A)\text{ OR }(\text{NOT }B). \]

Step 2: Examine the second Boolean expression. The second expression is \[ (A+B)'=A'B'. \] This states that the complement of the OR operation equals the AND operation of the individual complements. In words, \[ \text{NOT}(A \text{ OR } B) = (\text{NOT }A)\text{ AND }(\text{NOT }B). \]

Step 3: Identify the Boolean law represented. Both identities together form the pair of statements known as De Morgan's Laws. These laws are widely used for simplifying logical circuits and converting between NAND and NOR implementations. Conclusion: Therefore, the given Boolean expressions represent \[ \boxed{\text{De Morgan's Law}}. \]