A graph is a way of representing the relationships between elements in a set: an edge between the vertices \(x\) and \(y\) tells us that \(x\) is related to \(y\) (which we can write as \(x \sim y\)). Not all sorts of relationships can be represented by a graph though. For each relationship described below, either draw the graph or explain why the relationship cannot be represented by a graph.
The set \(V = \{1,2, \ldots, 9\}\) and the relationship \(x \sim y\) when \(x-y\) is a non-zero multiple of 3.
The set \(V = \{1,2, \ldots, 9\}\) and the relationship \(x \sim y\) when \(y\) is a multiple of \(x\text{.}\)
The set \(V = \{1,2,\ldots, 9\}\) and the relationship \(x \sim y\) when \(0 \lt |x-y| \lt 3\text{.}\)