#### Answer

The original statement makes sense. I'm working with a graph whose vertices are all even, so an Euler circuit must exist.

#### Work Step by Step

The original statement makes sense. I'm working with a graph whose vertices are all even, so an Euler circuit must exist.
According to Euler's theorem, if a graph has no odd vertices, then the graph has at least one Euler circuit. If a graph has vertices which are all even, then the number of odd vertices is zero. Therefore, according to Euler's theorem, there is at least one Euler circuit in the graph.