21.2. Example of an Equivalence Relation

Try these first

1. 1.

   What does it mean for a relation to be reflexive?

   Hint

   Think of a = a.

2. 2.

   Provide an example of a symmetric relation.

   Hint

   Consider how relationships often work.

3. 3.

   Which of the following properties is NOT required for a relation to be an equivalence relation?

   • Reflexivity
   • Symmetry
   • Irreflexivity

   Hint

   What does reflexivity indicate?

4. 4.

   True or false: If a is related to b and b is related to c, then a is definitely related to c.

   • True
   • False

   Hint

   What property does this describe?

5. 5.

   Formulate a real-world scenario that can be modeled as an equivalence relation and justify why it's an equivalence relation.

   Hint

   Consider how grading could show equivalence among students.

6. 6.

   Explore if the relation 'is a sibling of' on a set of individuals forms an equivalence relation. Discuss the properties.

   Hint

   Use logical family connections.