17.1.1. Definition and Characteristics

Try these first

1. 1.

   What is an irreflexive relation? Provide an example.

   Hint

   Think of pairs that don't include (a, a).

2. 2.

   Define a symmetric relation with an example.

   Hint

   Check for reciprocal pairs.

3. 3.

   What characterizes an irreflexive relation?

   • Elements relate to themselves
   • No elements relate to themselves
   • Some elements relate to themselves

   Hint

   Think about self-loops in a graph.

4. 4.

   Can a relation be both symmetric and irreflexive?

   • True
   • False

   Hint

   Imagine relations without self-connections.

5. 5.

   Consider the relation R = {(1, 2), (2, 3), (1, 3), (3, 1)}. Is it transitive, symmetric, or both? Justify your answer.

   Hint

   Check for flowing relationships versus reciprocal ones.

6. 6.

   Create a set and relation that is both antisymmetric and irreflexive, and explain your reasoning.

   Hint

   Think about the elements' distinctness and their relationships.