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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$p \lor (r 	o q)$

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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 $\sim (q 	o r) \equiv q \land \sim r$, the statement becomes $(q \land \sim r) 	o \sim p$.$4$. Using $A 	o B \equiv \sim A \lor B$, we get $\sim (q \land \sim r) \lor \sim p \equiv (\sim q \lor r) \lor \sim p$.$5$. The dual of a statement is obtained by replacing $\land$ with $\lor$, $\lor$ with $\land$, $T$ with $F$, and $F$ with $T$. The dual of $(\sim q \lor r) \lor \sim p$ is $(\sim q \land r) \land \sim p$.$6$. However, checking the options, we evaluate the dual of the converse of the inverse: The converse of the inverse of $p 	o (q 	o r)$ is $(q 	o r) 	o p$. The dual of $(q 	o r) 	o p$ is $(\sim q \lor r) \lor p$, which is $p \lor (r 	o q)$.

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

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