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: “Break the line, change the sign, and complement every variable.” AND becomes OR, OR becomes AND under negation.

Answer 1

The Correct Option is C

Concept: Boolean algebra is a branch of mathematics that deals with logical operations such as AND, OR, and NOT. Among its most important identities are De Morgan's laws, which describe how complementation interacts with AND and OR operations. These laws are widely used in digital circuit simplification and logic transformation.

Step 1: Analysis of $(AB)' = A' + B'$
The expression $(AB)'$ represents the complement of the AND operation between two variables $A$ and $B$. According to Boolean logic, when an AND expression is complemented, the result transforms into an OR expression where each variable is individually complemented. This gives: \[ (AB)' = A' + B' \] This transformation clearly shows that the operation changes from multiplication (AND) to addition (OR) while applying NOT to each variable separately. This is the fundamental statement of De Morgan's First Law.

Step 2: Analysis of $(A + B)' = A'B'$
The expression $(A + B)'$ represents the complement of the OR operation between $A$ and $B$. According to Boolean rules, when an OR expression is complemented, it becomes an AND expression where each variable is individually complemented: \[ (A + B)' = A'B' \] This is known as De Morgan's Second Law. It shows that OR changes to AND under complementation, with each variable being negated.

Step 3: Combined interpretation
Both expressions together form the complete set of De Morgan's laws. These laws are essential in switching between NAND-NOR logic implementations and simplifying complex logic circuits in digital electronics. Thus, the given expressions directly represent De Morgan's laws.