Perform the following operations for a Union$-$Find data structure:

$($When there's a tie for a union operation use alphabetical order on the roots so A$->$B$.)$

MakeSet$($A$),$ MakeSet$($B$),$ MakeSet$($C$),$ MakeSet$($D$),$ MakeSet$($E$),$ MakeSet$($F$),$ MakeSet$($G$),$ MakeSet$($H$),$ MakeSet$($I$)$

Union$($B$,$I$)$

Union$($D$,$G$)$

Union$($A$,$F$)$

Union$($C$,$H$)$

Union$($C$,$A$)$

Union$($A$,$G$)$

Union$($B$,$D$)$

a $)$ What is the rank$($I$)$ at the conclusion of these operations?

b $)$ What is $\backslash$pi $($H$)$ at the conclusion of these operations?

c$)$ What does a Find$($B$)$ return at the conclusion of these operations?