Part (a)
Let's assume the graph has $n$ vertices.
We take $n-1$ vertices and form a complete graph with it .
So the situation can be imagined as only one vertex is not touched by any edge and other $n-1$ vertices are connected in the best possible way .
If we add one more edge , this edge cannot be within the chosen $n-1$ vertices otherwise the graph won't be simple anymore , and adding an edge to the isolated vertex will connect it.
Thus we get a connected connected graph here.
Part (b)
We take $n=3$
A-B C and we get a disconnected graph here.