Question

In digital logic, what is the dual of the OR operation?

• A. NOT
• B. AND
• C. XOR
• D. NAND

Hint:

Duality → OR ↔ AND, 0 ↔ 1.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The principle of duality in Boolean algebra states that any logic identity remains valid if you swap operators and identity elements.
Step 2: Key Formula or Approach:
To find a dual:
1. Replace OR ($+$) with AND ($\cdot$).
2. Replace AND ($\cdot$) with OR ($+$).
3. Replace $0$ with $1$ and $1$ with $0$.
Step 3: Detailed Explanation:
The OR operation is represented as $A + B$.
Swapping the operator according to the duality rules gives $A \cdot B$, which is the AND operation.
Step 4: Final Answer:
The dual of OR is AND.