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?
Q: 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) A graph is viscous only if it satisfies condition (V).
(b) A graph is viscous if it satisfies condition (V).
(c) Foragraphtobeviscous,itisnecessarythatitsatisfiescondition (V).
(d) For a graph to be viscous, it is sufficient for it to satisfy condition (V).
(e) Satisfying condition (V) is a sufficient condition for a graph to be viscous.
(f) Satisfying condition (V) is a necessary condition for a graph to be viscous.
(g) Every viscous graph satisfies condition (V).
(h) Only viscous graphs satisfy condition (V).
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