Its image about my question which I want to solve but I have no idea how to solve it. Draw graph for each relation and say whether relation is a function or not.
Please make me understand how to solve this question.
2026-04-03 05:25:10.1775193910
Draw graph for each of the relation
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1
You will have a vertex for each element in your set (in your case a vertex representing each of the cities).
Then, for whichever specific relation you are looking at, draw an arrow (called a directed edge) from one vertex $x$ to another vertex $y$ if and only if $x$ is related to $y$. If it so happens that $x$ is related to $y$ and $y$ is related to $x$, you may either make the arrow double sided, or draw a separate arrow going in the opposite direction in addition to the first according to your personal preference. If an element is related to itself, draw a directed "loop" for the corresponding vertex, a curved arrow which leaves the vertex and turns around and points at the same vertex.
Such a graph represents a function iff every vertex has exactly one arrow leaving it. Similar properties of relations and functions can also be described from a graph theoritic point of view (*for example, bijective functions from a set to itself have exactly one arrow leaving and exactly one arrow arriving at each vertex*)