Let g(v, e) be an undirected connected graph, with positive costs ce on its edges. let g’(v, e) be the same graph as g, but the cost of each edge ‘e’ whose original cost in g was ce is replaced in g’ by ce 2 . for each of the following two statements, decide if it is true or false. if it is true, give a short explanation. if it is false, give a counter example. 

(a) if t is a minimum cost spanning tree of g, then t is a minimum cost spanning tree of g’. 

(b) wheres and t are distinct vertices of v, if p is a minimum cost s-t path in g, then p is a minimum cost s-t path in g’.