1.5. Properties of Posets and Total Ordering

Try these first

1. 1.

   Define an equivalence relation.

   Hint

   Consider the properties RST.

2. 2.

   Provide an example of a reflexive relation.

   Hint

   Think of situations where self-identity holds.

3. 3.

   What defines an equivalence relation?

   • Reflexive only
   • Reflexive
   • Symmetric
   • Transitive
   • Symmetric only

   Hint

   Recall the RST properties.

4. 4.

   Is the intersection of two equivalence relations an equivalence relation?

   • True
   • False

   Hint

   Consider reflexivity, symmetry, and transitivity.

5. 5.

   Given a set of five books with different genres, describe how you would establish an equivalence relation based on genre. Discuss if the union of two such relations would still retain properties.

   Hint

   Consider comparing relations across different categories.

6. 6.

   Construct a poset for a collection of shapes based on area and describe its total order. Are there specific comparisons missing?

   Hint

   Reflect on shapes' relative sizes while visualizing them.