Question

The dual of the statement pattern \( \sim p \land (q \lor t) \) is (where \( t \) is a tautology and \( c \) is a contradiction)

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

Hint:

While finding the dual of a logical statement, remember that negations remain unchanged.

Answer 1

The Correct Option is C

Step 1: Recall the principle of duality.
To find the dual of a statement:

Replace \( \land \) by \( \lor \) and \( \lor \) by \( \land \)
Replace tautology \( t \) by contradiction \( c \) and vice versa
Do not change negations

Step 2: Apply duality to the given statement.
Given statement: \[ \sim p \land (q \lor t) \] Dual statement becomes: \[ \sim p \lor (q \land c) \]

Step 3: Conclusion.
The dual of the given statement pattern is \[ \boxed{\sim p \lor (q \land c)} \]