Problem $2.$ Consider the three minimum spanning tree algorithms $($Borvka$,$ Jurn$$k$,$ and

Kruskal$)$ as presented in class or in lecture notes. Our proofs of correctness relied on the assumption

that the edge weights are distinct. State True$/$False for each of the following three statements. For

each of the statements, if you answer False, justify your answer with an example of a graph with

non$-$distinct edge weights that the algorithm fails to find its MST$.$

$($a$)$ Borvka correctly finds the MST of a graph with non$-$distinct edge weights.

$($b$)$ Jurn$$k correctly finds the MST of a graph with non$-$distinct edge weights.

$($c$)$ Kruskal correctly finds the MST of a graph with non$-$distinct edge weights.