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Math Help - equivalence relations

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    equivalence relations

    So this is a problem for one of my classes. I don't even know where to start...thanks for any help!

    Let A be a non-empty set, and let E1 and E2 be equivalence relations on A with associated partitions D1 and D2 , respectively. Let E be the equivalence relation on A defined by E = E1 ∩ E2 , and D its associated partition. Come up with a proposition describing the relationship between
    D1 , D2 and D. Prove your result.
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    Quote Originally Posted by junebug5389 View Post
    Let A be a non-empty set, and let E1 and E2 be equivalence relations on A with associated partitions D1 and D2 , respectively. Let E be the equivalence relation on A defined by E = E1 ∩ E2 , and D its associated partition. Come up with a proposition describing the relationship between D1 , D2 and D. Prove your result.
    Given an equivalence relation E on a set A, each cell in a partition determined by E is one of these sets: E_x  = \left\{ {y \in A:\left( {x,y} \right) \in E} \right\}.
    Therefore the partition determined by D is \left\{ {E1_x  \cap E2_x :x \in A} \right\}.
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