Let's say we have $7$ elements $($numbered $0$ to $6).$ Are the following matrices legal?

id array in Union$-$Finn? Justify! For those that are legal, they may have come up in

the weighted quick$-$union algorithm? Draw the trees in all cases and explain which ones

because of the matrix not come up increasingly Quick$-$union, or show a sequence of union operations

which end in this array.

a$.3,5,6,3,3,2,2$

b$.0,2,2,2,0,2,2$

c$.4,0,2,0,4,4,3$