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I am a beginner in this field. Actually, I am studying about equivalence relation. I found that the set of all equivalence relations possible on set A form a relation.

If R1 and R2 are two equivalence relations on set A, the least upper bound is given by trans($R1 \cup R2$) and the greatest lower bound is given by $R1 \cap R2$ where trans is the transitive closure.

I couldn't get what that means. Any insights examples that could help me?

I referred to this wiki article here

They have given the example of the is refinement of relation on the partitions of a set {1,2,3,4}. Since each partition has a corresponding equivalence relation, I want to know about the meet and join of the partitions.

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For eg in the above is given the lattice formed by the partitions of set {1,2,3,4}. I want to know if I want to find the join and meet of any two elements in the lattice lets say

1/2/3/4 and 1/23/4 then what would the join and meet be for these two elements? And what it means when it says least upper bound and greatest lower bound

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    Don't you mean $R_1\cup R_2$ and $R_1\cap R_2$?2012-09-12
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    Yeah. I have changed it2012-09-12
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    But $R_1\cup R_2$ is not necessarily an equivalence relation! Try $\bigcap\{R\mid R\mathrm{\ is\ eq.rel.}, R_1\cup R_2\subseteq R\}$ instead.2012-09-12

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