The dual of the statement pattern (p land sim | vedclass

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(C) Step $1$: To find the dual of a statement pattern, replace $\land$ with $\lor$, $\lor$ with $\land$, $T$ with $F$, and $F$ with $T$. Note that the

Vedclass · Accepted Answer

$(\sim p 	o q) \land (q 	o p)$

Vedclass · Answer

(C) Step $1$: To find the dual of a statement pattern, replace $\land$ with $\lor$, $\lor$ with $\land$, $T$ with $F$, and $F$ with $T$. Note that the implication $	o$ is not a basic connective, so we rewrite the statement using $\land, \lor, \sim$ first.Step $2$: The statement is $(p \land \sim q) 	o (q \land \sim p)$. Since $A 	o B \equiv \sim A \lor B$, the statement becomes $\sim (p \land \sim q) \lor (q \land \sim p)$.Step $3$: Applying De Morgan's law, $\sim (p \land \sim q) \equiv \sim p \lor q$. So the statement is $(\sim p \lor q) \lor (q \land \sim p)$.Step $4$: The dual of $(\sim p \lor q) \lor (q \land \sim p)$ is $(\sim p \land q) \land (q \lor \sim p)$.Step $5$: This simplifies to $(\sim p \land q) \land (\sim p \lor q)$. This is equivalent to $\sim p \land q$, which is $\sim (p \lor \sim q)$.Step $6$: Checking the options, the dual of the original expression $(p \land \sim q) 	o (q \land \sim p)$ is $(p \lor \sim q) \land (q \lor \sim p)$ (replacing $	o$ with $\lor$ and $\land$ with $\lor$).Step $7$: The correct dual is $(p \lor \sim q) \land (q \lor \sim p)$, which is equivalent to $(\sim p 	o q) \land (q 	o p)$.

The dual of the statement pattern $(p \land \sim q) \to (q \land \sim p)$ is equivalent to

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