0
$\begingroup$

Consider the equivalence relation between non-empty subsets $A , B$ of $\{ 1,2,3, 4,\dots,100\}$ defined by the condition:

the greatest element of $A$ is the same as the greatest element of $B .$ Let $P$ be the partition corresponding to this equivalence relation. What are the elements of $P$?

Can someone please explain this question to me? Does the first line means we can have any element in $ A$ and $B$ as long as the greatest of both are equal? and what is $P$ that corresponds to the equivalence relation? What is the equivalence relation?

$\endgroup$
0
$\begingroup$

Hint: Here is one equivalence class (which in turn is a set of the partition): $\{\{3\},\{1,3\},\{2,3\},\{1,2,3\}\}$. This set of the partition contains all subsets of $\{1,2,\dots,100\}$ with max element $3$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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