0
$\begingroup$

I have a set L and I have a subset S which is part of L and contains three elements A, B and C. Finally, each of these elements are subsets that consist of their own elements:

$A=\{a_1...a_n\}$

$B=\{b_1...b_n\}$

$C=\{c_1...c_n\}$

A, B and C contain the same number of elements and those elements stand in a binary relation.

What I want to do is to specify that A, B and C consists of 'several' elements. 'Several' here means that there is at least one element and at most the number of elements which are smaller than L.

This is my attempt:

$S=\{x_ i | 1\le\ i\ \lt\ L\} $

where I use x to denote all elements from A, B and C and i to denote the number of elements.

I think that a link is missing here between the final representation and subsets A, B and C. Any suggestion how to deal with this? Thanks.

$\endgroup$
1
$\begingroup$

The number of elements of a set A, called the cardinality of A is denoted $|A|$. Here's what I understand you are trying to say:

I have a set $L$ and a set $S$ which is a subset of $L$. $S$ is the set $\{A, B, C\}$, where: $$A = \{a_1, a_2, ... a_n\}$$ $$B = \{b_1, b_2, ... b_n\}$$ $$C = \{c_1, c_2, ... c_n\}$$ for some integer $n$ such that $1 \le n \lt |L|$.

$\endgroup$

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.