option A: False
There exists an independent set of size ∣C∣
This may not be true always as the independent set can be empty .ie, all the vertices may be included in the vertex cover( even both the end points of every edge as it is not a minimum vertex cover).
option B True
For any graph V(G)−C is an independent set
Reason: there will be no edge between the vertices of I set as per the definition of vertex cover. There is no edge with both sides belonging to independent set(if so then the subset is not vertex cover)
option C & D can be proved wrong using a complete graph with a vertex in the centre.
option E : False
Consider a graph with an isolated vertices. It falls in independent set. So intersection is empty.