Relation
Task number: 3838
The relation “an oriented path from \( u \) to \( v \) exists” on the vertices of the following oriented graph is
- symmetric but not transitive;
- transitive but not symmetric;
- symmetric and transitive.
Solution
In the above graph, there is an oriented path between every two vertices, so both properties are satisfied.
In the general case, transitivity always applies (by concatenation ob paths and omitting unnecessary subpaths), byt symmetry may not hold.
Answer
The correct answer is c.
