Let ( R ) be an equivalence relation on ( A ). Given ( a in A ), define ( [a] ) to be the set [ [a]= {b in A mid(a, b) in R } . ] Show that ( {[a] mid a in A } ) is a partition of ( A ).

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Let  ( R  ) be an equivalence relation on  ( A  ). Given  ( a  in A  ), define  ( [a]  ) to be the set  [ [a]= {b  in A  mid(a, b)  in R } .  ] Show that  (  {[a]  mid a  in A }  ) is a partition of  ( A  ).

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(Solved): Let \( R \) be an equivalence relation on \( A \). Given \( a \in A \), define \( [a] \) to be the ...

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