मंजिलें बड़ी जिद्दी होती हैं, हासिल कहां नसीब से होती हैं।

मगर वहां तूफान भी हार जाते हैं, जहां कश्तियां जिद्द पे होती हैं।।

**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.