Let G be a graph with no isolated vertices, and let M be a maximum matching of G. For each vertex v not saturated by M, choose an edge incident to v. Let T be the set of all the chosen edges, and let L = M ∪ T. Which of the following option is TRUE?

Given answer is C. I was also thinking A. It would not result in min. edge cover right?

The explanation given by them is-

Both statements are true.

(A) This construction of L is exactly the one in the proof of a theorem. L is an edge cover by construction, since all edges not saturated by M are covered by the additional edges T; and it is a minimum one because its size is

n−|M| = n−α'(G) = β'(G)

by the theorem.

For option (B), it has no superfluous edges that can be removed from it and still have a edge cover, but this does not prove that L is minimum.

Option (C) is correct choice.

I am not able to understand this. they are saying it is minimum in (A). And then in (B) they say "this does not prove that L is minimum".

Is anyone getting what they are trying to explain through this-