An undirected graph is connected when it has at least one vertex and there is a path between every pair of vertices. Equivalently, a graph is connected when it has exactly one connected component.
In that case a,b,c,d, x,y all are vertices and the graph is connected hence all must have a path between them since its a connected graph, hence A,B,C should be true as per defination.
I couldn't find any such graph which has a P1 and P2 as such and has no vertex is common so i find D is also true.
Plz comment on the above