The dual of a boolean expression is obtained by interchanging OR and AND operations and interchanging 0s and 1s. 

Given the expression \( A + B + C \):

### Steps to find the dual:

1. Interchange \( + \) (OR) with \( \cdot \) (AND).
2. Replace any \( 0 \) with \( 1 \) and any \( 1 \) with \( 0 \).

For the expression \( A + B + C \):

- The OR operation \( + \) becomes the AND operation \( \cdot \).

Thus, the dual of \( A + B + C \) is:

\[
A \cdot B \cdot C
\]

### Explanation:

- Original expression: \( A + B + C \)
- Dual expression: \( A \cdot B \cdot C \)

Would you like more details or have any questions?

Here are 8 related questions to consider:

1. How do you find the dual of more complex boolean expressions?
2. What is the significance of duality in boolean algebra?
3. Can you provide an example of duality in real-world digital circuits?
4. How do De Morgan's laws relate to the concept of duality?
5. What is the dual of the expression \( (A \cdot B) + (C \cdot D) \)?
6. How do you apply duality to NAND and NOR gates?
7. What are some practical applications of using dual expressions in circuit design?
8. How does duality help in simplifying boolean expressions?

**Tip:** Understanding the concept of duality in boolean algebra can significantly aid in the design and simplification of digital logic circuits.

Learn how to find the dual of the boolean expression A + B + C in Boolean algebra. Understand the steps involved in interchanging OR and AND operations and replacing 0s with 1s and 1s with 0s. Suitable for anyone studying Boolean algebra or digital logic circuits.

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