Equivalence Classes of An Equivalence Relation
Category : JEE Main & Advanced
Let R be equivalence relation in \[A(\ne \varphi )\]. Let \[a\in A\]. Then the equivalence class of \[a,\] denoted by \[[a]\] or \[\{\bar{a}\}\] is defined as the set of all those points of A which are related to a under the relation R. Thus \[\left[ a \right]\text{ }=\text{ }\{x\hat{I}A:x\text{ }Ra\}.\]
It is easy to see that
(1) \[b\in [a]\Rightarrow a\in [b]\]
(2) \[b\in [a]\Rightarrow [a]=[b]\]
(3) Two equivalence classes are either disjoint or identical.
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