Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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

share|improve this question

1 Answer 1

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.

share|improve this answer
    
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

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.