1
$\begingroup$

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 $a = (0, 0, 1, 0, 1, 1, 0, 1) \in A$)?

1 Answers 1

1

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.

  • 0
    Is that it? Thank you for the help! The answer wasn't immediately visible to me, but now I see what to do.2012-10-31