17.1.2. Examples of Irreflexive Relations

Try these first

1. 1.

   Is the relation R = {(1, 2), (2, 1)} irreflexive for set A = {1, 2}?

   Hint

   Check if any pairs (a, a) exist.

2. 2.

   What entry in the matrix representation of an irreflexive relation would you expect for (1, 1)?

   Hint

   Remember, we are looking for self-relating pairs.

3. 3.

   What defines an irreflexive relation?

   • (a
   • a) is present
   • (a
   • a) is absent
   • May or may not have (a
   • a)

   Hint

   Think about the definition of irreflexive.

4. 4.

   True or False: The empty relation is both reflexive and irreflexive.

   • True
   • False

   Hint

   Consider the definition of these terms in a void scenario.

5. 5.

   If A = {x, y, z} and R = {(x, y), (y, z), (x, z)}, classify R as reflexive or irreflexive. Justify your answer.

   Hint

   Check each element in A.

6. 6.

   Provide an example of a relation R from a set A = {1, 2, 3} that is irreflexive and also explain the matrix representation.

   Hint

   Ensure no self-relating pairs are included.