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।।

Lecture - 2 Relations and Functions

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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