# For Each Of The Following Two Statements Decide Whether It Is True Or False If

“For each of the following two statements, decide whether it is true or false. If true, give a short explanation. If false provide a counterexample.a) Suppose we are given an instance of the Minimum Spanning Tree Problem on a graph G, with edge costs that are all positive and distinct. Let T be a minimum spanning tree for this instance. Now, suppose we replace each edge cost Ce by its square, Ce^2, thereby creating a new instance of the problem with the same graph but different costs.True or false? T must still be a minimum spanning tree for this new instance.b) Suppose we are given an instance of the Shortest s-t Path problem on a directed graph G. We assume that all edge costs are positive and distinct. Let P be a minimum cost s-t path for this instance. Now suppose we replace each edge cost Ce with its square, Ce^2, thereby creating a new instance of the problem with the same graph but different costs.True or false? P must still be a minimum cost s-t path for this new instance. ”

Ans 2 1: if there is cost b/w………..0&lt;Ce&lt;1;then there may be change MST &quot;T&quot;So I think it is false. But we also check the following condition:In kruskal’s algorithm, it is…

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