Discussion
The dual statement of \(p \Rightarrow q \wedge r\) is :
Answer: D
The dual statement is \(((\sim p) \wedge q) \vee ((\sim p) \wedge r)\).
The dual is formed from an expression in \(\wedge\), \(\vee\) and \(\sim\) by swapping \(\wedge\) with \(\vee\). First remove the implication:
\[ p \Rightarrow q \wedge r \equiv (\sim p) \vee (q \wedge r) \]
Its dual is \((\sim p) \wedge (q \vee r)\), and distributing \(\sim p\) over the disjunction gives \(((\sim p) \wedge q) \vee ((\sim p) \wedge r)\), option D.
Option B is \((\sim p) \vee (q \vee r)\), which swaps only the inner connective. Option A leaves \(p\) unnegated, and option C negates the wrong letters.
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