:$.$ The state set of a synchronous reactive component is $\{0,1,$dots,$7\}.$ Each state is encoded as its binary number $xyz$ where $x,y$ and $z$ are boolean type variables.

$($a$)$ What is the state subset represented by the expression

$(x^{{?}^{?}}y)vv(not{x}^{{?}^{?}}{y}^{{?}^{?}}z)vv(x^{{?}^{?}}z)?$

$($b$)$ Represent the expression in $($a$)$ with an ordered BDD following the ordering $x.$

$(c)$ Convert the ordered $BDDin(b)to$ the canonical ROBDD.