Figure $6\mathrm{.}9($page $367)$ shows a BDD with ordering $[$x$,$ y$,$ z$].$

$*$ F $($a$)$ ind an equivalent reduced BDD with ordering $[$z$,$ y$,$ x$].($Hint: find first the

decision tree with the ordering $[$z$,$ y$,$ x$],$ and then reduce it using C$1$C$3.)$

$($b$)$ Carry out the same construction process for the variable ordering $[$y$,$ z$,$ x$].$

Does the reduced BDD have more or fewer nodes than the ones for the

orderings $[$x$,$ y$,$ z$]$ and $[$z$,$ y$,$ x$]?$Figure $6\mathrm{.}9.$ A BDD representing the same function as the BDD of

Figure $6\mathrm{.}7,$ but having the variable ordering $x,y,z.$