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.

https://en.wikipedia.org/wiki/Connectivity_(graph_theory)

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