Logics for this lecture:

•A relation R on set A is said to be
reflexive if \( (a, a) \in R, \forall a \in A \text{ or }  aRa, \forall a \in A \)
symmetric if \( (a, b) in R \Rightarrow (b, a) \in R, \forall a, b \in A \text{ or }  aRb \Rightarrow bRa, \forall a, b \in A \)
transitive if \( (a, b) \in R, (b, c) \in R \Rightarrow (a, c) \in R, \forall a, b, c \in A \text{ or }  aRb \text{ and } bRc, \Rightarrow aRc, \forall a, b, c \in A \)
•If a relation is reflexive, symmetric and transitive then the relation is said to be equivalence relation.
• An important property of an equivalence relation is that it divides the set into pairwise disjoint (or mutually disjoint) subsets called equivalence classes whose collection is called a partition of the set.
• The union of all equivalence classes gives the whole set.