How do i approach this problem?
Let G represent a graph with vertices V. The only atomic statements about the graph are of the form G(v,w) where v and w are vertices in V and G(v,w) means there is an edge between v and w. The quantifiers ∀x and ∃x refer to the vertex set V. With this context, express the following statements about the graph G formally using quantifiers and atomic statements:
- There is some vertex in the graph that has an edge connecting it to every other vertex.
- The graph is the complete graph.
- Any two vertices are connected by a path of length 3.
- The graph contains no triangle.
- Among any four vertices at least two are connected by an edge.