Let $G$ be a simple graph with $20$ vertices and $100$ edges. The size of the minimum vertex cover of $G$ is $8$. Then, the size of the maximum independent set of $G$ is:

If S is the vertex cover of G, then remaining vertices V-S must form an independent set
i.e Vertex Cover + Size of Max Independent Set = Total no of Vertices

Here Vertex Cover is 8 and Total no of Vertices are 20. so size of Max Independet set is 20-8 = 12

An Independent Set is a set of vertices (of a graph), such that they're not adjacent to each other in the graph.

A Maximal independent set is the maximum sized independent set.

Here, {1,5} is an independent set.

{1,4,5,6} is Maximal Independent Set.

Clique

Clique is the exact opposite of an Independent set.

Clique is a set of vertices (of a graph), such that they're all adjacent to each other in the graph.

{2,4,5,7} is a clique

Vertex-Cover

Vertex-cover is a set of vertices (of a graph), such that all the edges in the graph are incident on some vertex in it. In other words, the set of vertices that "cover" each edge.

Now, coming to the question, we can observe some things here:-

Maximal Independent Set + Minimal Vertex-Cover = All the vertices. (Evident from Image-1 and Image-3)

So, $8+x=20$ $=> x=12$

Option A

More:-

A set S is independent iff V-S is a vertex-cover.
=> If a set of vertices is vertex-cover (minimal or not) the remaining vertices together form an independent set. And vice versa.

A set S is independent in G iff S is a clique in G'. Evident from their definitions.