Introduction:
In this problem, we are given a graph G with 2n vertices, where each vertex corresponds to a subset of a set of size n. Two vertices are adjacent if and only if the corresponding subsets intersect in exactly two elements.

Understanding the problem:
To solve this problem, we need to find the number of connected components in the graph G.

Approach:
To find the number of connected components in the graph G, we can use the concept of disjoint sets.

Step 1: Create a disjoint set for each vertex:
- Create a disjoint set for each vertex of the graph G.
- Initially, each vertex is in its own disjoint set.

Step 2: Merge disjoint sets:
- For each pair of vertices that are adjacent in the graph G, merge their corresponding disjoint sets.
- This can be done by finding the root of each disjoint set using the find operation and then merging the two sets using the union operation.

Step 3: Count the number of disjoint sets:
- After merging all the disjoint sets, count the number of disjoint sets remaining.
- Each disjoint set represents a connected component in the graph G.

Explanation:
In this problem, each vertex of the graph G corresponds to a subset of a set of size n. Let's consider an example with n = 3 to understand the concept.

For n = 3, the graph G will have 2n = 6 vertices, each corresponding to a subset of a set of size 3.

The subsets corresponding to the vertices are as follows:
- Vertex 1: {}
- Vertex 2: {1}
- Vertex 3: {2}
- Vertex 4: {3}
- Vertex 5: {1, 2}
- Vertex 6: {1, 3}

Now, let's determine the adjacency between vertices based on the intersection of their corresponding subsets.

- Vertex 1 and Vertex 2: The intersection of {} and {1} is {} which has exactly two elements. Hence, Vertex 1 and Vertex 2 are adjacent.
- Vertex 1 and Vertex 3: The intersection of {} and {2} is {} which has exactly two elements. Hence, Vertex 1 and Vertex 3 are adjacent.
- Vertex 1 and Vertex 4: The intersection of {} and {3} is {} which has exactly two elements. Hence, Vertex 1 and Vertex 4 are adjacent.
- Vertex 1 and Vertex 5: The intersection of {} and {1, 2} is {} which has exactly two elements. Hence, Vertex 1 and Vertex 5 are adjacent.
- Vertex 1 and Vertex 6: The intersection of {} and {1, 3} is {} which has exactly two elements. Hence, Vertex 1 and Vertex 6 are adjacent.
- Vertex 2 and Vertex 3: The intersection of {1} and {2} is {} which does not have exactly two elements. Hence, Vertex 2 and Vertex 3 are not adjacent.
- Vertex 2 and Vertex 4: The intersection of {1} and {3} is {} which does not have exactly two elements. Hence, Vertex 2 and Vertex 4 are not adjacent.
- Vertex 2 and Vertex 5: The intersection of {1} and {1