Proving an equivalence relation from partitions

Asked Jul 19 '23 at 19:55

Active Jul 19 '23 at 19:55

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Equivalence relations from partitions A set S is given as a union $S=\bigcup_{i} S_i$ of mutually disjoint subsets $S_i$. Define a relation on S by declaring $s,\tilde{s} \in S$ as related if they are contained in the same subset $S_i$. Show that this is an equivalence relation, which partitions S into the subsets $S_i$.

Could I get some advice or hints on how to start and understand what the problem is asking?

asked Jul 19 '23 at 19:55

CarlGaussian

Not a site for homework, besides have you tried to use the definitions? It's direct – julio_es_sui_glace Jul 19 '23 at 19:59
it's just straightforward definition checking really. – UnsinkableSam Jul 19 '23 at 20:01
It will not necessarily be a partition unless one assumes all subsets $S_i$ are nonempty. – coffeemath Jul 19 '23 at 20:01
@coffemath: At least some definitions of "partition" include nonemptiness of the partitioning subsets. https://en.wikipedia.org/wiki/Partition_of_a_set – paw88789 Jul 19 '23 at 20:08

Proving an equivalence relation from partitions

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