Let w be the minimum weight among all edge weights in an un-directed connected graph. Let e be a specific edge of weight w. Which of the following statements is/are TRUE/FALSE? Please discuss each of...

Let w be the minimum weight among all edge weights in an un-directed connected graph. Let e be a specific edge of weight w.

Which of the following statements is/are TRUE/FALSE? Please discuss each of these statements on why that statement is True/False.

a.   Every minimum spanning tree has an edge of weight w
b.   If e is not in a minimum spanning tree T, then in the cycle formed by adding e to T, all edges have the same weight
c.   There is a minimum spanning tree containing e.
d.   e is present in every minimum spanning tree