I'm posting this question and answers to see if I am on the right track here, just want to be sure I understand or don't understand.
Bellow I will list some equivalence relations over the set $ S= \{1,2,3,4\} $ the assignment is to find the equivalence classes to $ [1] $
$\{<1,1>,<2,2>,<3,3>,<4,4>\}, [1] = \{1\}$
$\{<1,1>,<2,2>,<3,3>,<4,4>,<1,2>,<2,1>\}, [1] = \{1,2\}$
$\{<1,1>,<2,2>,<3,3>,<4,4>,<1,3>,<3,1>\}, [1] = \{1,3\}$
$\{<1,1>,<2,2>,<3,3>,<4,4>,<1,4>,<4,1>,<2,3>,<3,2>\}, [1] = \{1,4\}$
$\{<1,1>,<2,2>,<3,3>,<4,4>,<2,3>,<3,2>\}, [1] = \{1\}$
$\{<1,1>,<2,2>,<3,3>,<4,4>,<1,2>,<1,4>,<2,1>,<2,4>,<4,1>,<4,2>\}, [1] = \{1,2,4\}$
So if my answers are correct then great, if not what do I need to look at?
Cheers
It is right except the first relation: it is not an equivalence (maybe you forgot to write $<4,4>$).