Equivalence relations and classes problem.

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Homework Statement


Let X = {a,b,c,d}. How many different equivalence relations are there on X? What subset of
XxX corresponds to the relation whose equivalence classes are {a,c},{b,d}



Homework Equations



N/A

The Attempt at a Solution



So I wrote out all the possible "blocks" and it comes to 15 which is the bell number B4 = 15 so thats correct.

My problem comes from the second part of the question because I'm unsure what its asking. Is it just asking for the 15 different partitions possible which one is related to {a,c},{b,d} ?

if that is the case isn't it just {{a,c},{b,d}} ~ {a,c,{b,d}} ?

Thanks in advance
 

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