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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:

  1. There is some vertex in the graph that has an edge connecting it to every other vertex.
  2. The graph is the complete graph.
  3. Any two vertices are connected by a path of length 3.
  4. The graph contains no triangle.
  5. Among any four vertices at least two are connected by an edge.

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