mad3105 asgn3

MAD3105 Asgn3 - Equivalence Relations

Def.
Equivalence Relations: a relation that is reflexive, symmetric, and transitive

Ex. Set A = {a, b, c, d} & Relation R = {(a,a), (c,c), (c,d), (d,d), (b,d), (d,c)
- R would not be an equivalence relation because it is not reflexive, nor it is symmetric, nor is it transitive.

Def.
Set partition: a set of subsets of a set A that contain all of the elements of the original sets without duplicates

Ex. Set A = {a, b, c, d}
- Partition A = {{a,b}, {c}, {d}}
- Nonpartition B = {{a,b,c}, {d}, {a,b}}
-> A contains all elements w/o dupes, B contains all elements plus dupes of a,b