$6.$ Assume that a compound proposition contains only $\backslash (\backslash$mathrm$\{$V$\},\backslash$mathrm$\{\backslash$Lambda$\}\backslash$rightarrow $\backslash )$ operators. Daal of such a compound proposition is obtained by replacing each $\backslash ($ V $\backslash )$ with $\backslash ($ A $\backslash )$ and each $\backslash (\backslash$Lambda $\backslash )$ with $\backslash ($ V $\backslash ).$ We also replace $\backslash ($ T $\backslash )$ with $\backslash ($ F $\backslash )$ and $\backslash ($ F $\backslash )$ with $\backslash ($ T $\backslash )$ in the original proposition.$($a$)$ What is the dual of $\backslash ($ p $\backslash$vee$($q $\backslash$vee$($r $\backslash$wedge T$))\backslash )($b$)$ Once again, assume two compound propositions $\backslash ($ P$,$ Q $\backslash ).$ They contain only $\backslash ($ V$,$ A$,-\backslash )$ operators. Suppose $\backslash ($ P$=$Q$,1\backslash )$ is$.\backslash ($ P $\backslash )$ is the same $($equivalent$)$ as $\backslash ($ Q $\backslash ).$ Is it the case that the duals of $\backslash ($ P $\backslash )$ and $\backslash ($ P$,$ Q $\backslash )$ which are equivalent are not equivalent.