22.1.1. Lecture -22

Try these first

1. 1.

   Define a partition of the set {1, 2, 3, 4}.

   Hint

   Make sure to include non-empty disjoint subsets.

2. 2.

   True or False: In a partition, two subsets can overlap.

   Hint

   Remember the definition of disjoint subsets.

3. 3.

   What defines an equivalence relation?

   • Reflexive
   • symbiotic
   • Reflexive
   • symmetric
   • transitive
   • Asymmetric and cyclic

   Hint

   Think about the properties you learned.

4. 4.

   True or False: A partition can contain empty subsets.

   • True
   • False

   Hint

   Refer to the definition of partitions.

5. 5.

   Given the set $C = \{a, b, c, d, e, f\}$ and the partition $P = \{\{a, b\}, \{c, d, e\}, \{f\}\},$ construct the equivalence relation and prove its properties.

   Hint

   Check the conditions for creating pairs from subsets within the partition.

6. 6.

   Determine the number of possible partitions for the set $\{1, 2, 3, 4\}$.

   Hint

   Think about all the ways to combine and split into disjoint non-empty subsets.