You have discovered an old paper on graph theory that discusses the
viscosity of a graph (which for all you know, is something completely made up by the author). A theorem in the paper claims that “if a graph satisfies
condition (V), then the graph is
viscous.” Which of the following are equivalent ways of stating this claim? Which are equivalent to the
converse of the claim?
- A graph is viscous only if it satisfies condition (V).
- A graph is viscous if it satisfies condition (V).
- For a graph to be viscous, it is necessary that it satisfies condition (V).
- For a graph to be viscous, it is sufficient for it to satisfy condition (V).
- Satisfying condition (V) is a sufficient condition for a graph to be viscous.
- Satisfying condition (V) is a necessary condition for a graph to be viscous.
- Every viscous graph satisfies condition (V).
- Only viscous graphs satisfy condition (V).