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Let $A=\{0,1\}^8$ with equivalence relation $R$ on $A$ as

$R=\{(u,v)∈A×A|\text{u and v have the same number of entries equal to 0}\}$

How do I find $[(0, 0, 1, 0, 1, 1, 0, 1)]$ (the equivalence class for $a = (0, 0, 1, 0, 1, 1, 0, 1) \in A$)?

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up vote 2 down vote accepted

Having shown that $R$ is indeed an equivalence relation, the equivalence class of an element $a\in A$ is simply the set of all elements in $A$ that are related to $a$. In this case, it is the set of all elements in $A$ with exactly $4$ zero entries.

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Is that it? Thank you for the help! The answer wasn't immediately visible to me, but now I see what to do. – user41419 Oct 31 '12 at 6:13

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