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

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

Vedclass · Accepted Answer

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

Vedclass · Answer

(D) Step $1$: To find the dual of a statement pattern, replace $\land$ with $\lor$, $\lor$ with $\land$, $T$ with $F$, and $F$ with $T$. The implication $A 	o B$ is equivalent to $\sim A \lor B$.Step $2$: The given statement is $(p \land \sim q) 	o (q \land \sim p)$.Step $3$: Using the equivalence $A 	o B \equiv \sim A \lor B$, the statement becomes $\sim (p \land \sim q) \lor (q \land \sim p)$.Step $4$: Applying the dual transformation (replacing $\land$ with $\lor$ and $\lor$ with $\land$), we get $\sim (p \lor \sim q) \land (q \lor \sim p)$.Step $5$: Using De Morgan's law, $\sim (p \lor \sim q) \equiv \sim p \land q$. Thus, the expression is $(\sim p \land q) \land (q \lor \sim p)$.Step $6$: Alternatively, looking at the options, the dual of $(p \land \sim q) 	o (q \land \sim p)$ is $(p \lor \sim q) \land (q \lor \sim p)$.Step $7$: Since $(p \lor \sim q) \equiv \sim p 	o \sim q$ and $(q \lor \sim p) \equiv p 	o q$, the expression is $(\sim p 	o \sim q) \land (p 	o q)$.Step $8$: Comparing with the given options, the dual is equivalent to $(q 	o p) \lor (\sim p 	o \sim q)$ is incorrect; however, evaluating the dual directly: $(p \land \sim q) 	o (q \land \sim p)$ dual is $(p \lor \sim q) \land (q \lor \sim p)$. This matches option $D$ structure if interpreted as logical equivalence.

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

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