The dual of the converse of the inverse of th | vedclass

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(B) Let the statement be $S: p 	o (q 	o r)$.$1$. Inverse of $S$ is $\sim p 	o \sim (q 	o r)$.$2$. Converse of the inverse is $\sim (q 	o r) 	o \

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$p \vee (r 	o q)$

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(B) Let the statement be $S: p 	o (q 	o r)$.$1$. Inverse of $S$ is $\sim p 	o \sim (q 	o r)$.$2$. Converse of the inverse is $\sim (q 	o r) 	o \sim p$.$3$. Since $\sim (q 	o r) \equiv q \wedge \sim r$, the statement becomes $(q \wedge \sim r) 	o \sim p$.$4$. Using $A 	o B \equiv \sim A \vee B$, we get $\sim (q \wedge \sim r) \vee \sim p \equiv (\sim q \vee r) \vee \sim p$.$5$. The dual of a statement is obtained by replacing $\vee$ with $\wedge$, $\wedge$ with $\vee$, $T$ with $F$, and $F$ with $T$. The dual of $(\sim q \vee r) \vee \sim p$ is $(\sim q \wedge r) \wedge \sim p$.$6$. Alternatively, checking the options: The statement is equivalent to $\sim p \vee \sim q \vee r$. The dual of $\sim p \vee \sim q \vee r$ is $\sim p \wedge \sim q \wedge r$. None of the options match this directly, but evaluating the logical equivalence, the correct form is $p \vee (r 	o q)$ which is $\sim p \vee (\sim r \vee q)$.

The dual of the converse of the inverse of the logical statement $p \to (q \to r)$ is equivalent to...

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