Consider the Boolean function $f=a_1{b}_1+a_2{b}_2+$dots$+a_n{b}_n.$

$($a$)$ Show that the ROBDD under variable ordering index index$(b_n)2n+{22}^{n+1}$index$(b_1)$ has $2^{n+1}$ nodes.$(a_1)$

index$(b_1)$ has $2^{n+1}$ nodes.$(a_1)$

index$(b_n)$ has $2n+2$ nodes.

$(b)$ Show that the ROBDD under variable ordering index $(a_1)$

index$(b_1)$ has $2^{n+1}$ nodes.