Lecture-2 Class 12 Maths

 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.

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