Question

The dual of statement \( t \lor (p \lor q) \) is _________.

• A. \( c \land (p \lor q) \)
• B. \( c \land (p \land q) \)
• C. \( t \land (p \land q) \)
• D. \( t \land (p \lor q) \)

Hint:

In duality, exchange \( \lor \) with \( \land \) and vice versa, ensuring the variables remain in the same order.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept of Duality 
Duality in logic involves the following transformations: 
- Replacing \( \lor \) (OR) with \( \land \) (AND), and vice versa. 
- Swapping \( 1 \) with \( 0 \), and vice versa. 
Step 2: Applying Duality to the Given Expression 
For the expression \( t \lor (p \lor q) \), applying the duality principle gives: \[ t \lor (p \lor q) \quad \Rightarrow \quad t \land (p \land q) \] Hence, the correct result is \( t \land (p \land q) \).