22.1. Discrete Mathematics

Try these first

1. 1.

   What is the definition of a partition?

   Hint

   Think about how you can divide something into parts that don’t overlap.

2. 2.

   Give an example of an equivalence relation.

   Hint

   Consider how numbers relate to each other.

3. 3.

   What is an equivalence relation?

   • A relation that is only symmetric.
   • A relation that is reflexive
   • symmetric
   • and transitive.
   • A relation that has no properties.

   Hint

   Remember RST for Reflexive, Symmetric, Transitive.

4. 4.

   True or False: Partitions can overlap.

   • True
   • False

   Hint

   Think about the definition of partition again.

5. 5.

   Create a set of students and partitions them into groups based on their favorite colors. Then define an equivalence relation based on this partition.

   Hint

   Think how to relate members based on their color preference.

6. 6.

   Given the equivalence relation R on set A where R = {(1, 1), (2, 2), (1, 2), (2, 1)}. Determine the equivalence classes and show they form a partition.

   Hint

   Identify how members relate to each other under R.