16.3.1. Reflexive Relations

Try these first

1. 1.

   Is a relation with the pairs {(1,1), (2,2)} reflexive?

   Hint

   Check if both elements relate to themselves.

2. 2.

   Can the empty relation be reflexive?

   Hint

   Consider what it means to have no elements.

3. 3.

   What defines a reflexive relation?

   • Every element relates to a different one.
   • Every element relates to itself.
   • Some elements relate to themselves.

   Hint

   Think about the meaning of 'reflexive'.

4. 4.

   If a relation R is reflexive, which of the following is true?

   • True
   • False

   Hint

   Remember how to represent relations with matrices.

5. 5.

   Given a set A = {1, 2, 3}, create a non-empty reflexive relation. What pairs must it contain?

   Hint

   Focus on the requirement of self-pairings.

6. 6.

   Formulate a scenario where an empty relation can be considered reflexive. Describe the implications.

   Hint

   Think about the conditions that make a relation valid.