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Apr22-05, 04:36 PM
Sci Advisor
PF Gold
Hurkyl's Avatar
P: 16,091
That's not correct. For example, take this graph:

A B---C

This graph has three vertices and one edge.

Your statement "Ex Ey: ~edge(x, y)" is true for this graph -- for example, I can select x=A and y=B, and then "~edge(A, B)" is a true statement. However, the graph obviously does not have zero edges!

In English, your statement says: "There exists a pair of vertices that don't have an edge between them". Do you see why?