1
$\begingroup$

Say I have 2 sets of sets:

$$ X = \left \{ \left \{ 1,2 \right \}, \left \{ 3,4 \right \} \right \} $$ $$ Y = \left \{ \left \{ 1,3 \right \}, \left \{ 2,4 \right \} \right \} $$

I want to express that each sub-set of x has at least 1 element in common with each subset of y.

Here is what I came up with:

$$ \left \| x \cap y \right \| \geq 1, \forall x \in X, \forall y \in Y $$

Does this seem correct?

$\endgroup$
5
  • 3
    $\begingroup$ Seems good to me $\endgroup$
    – Mike Earnest
    Nov 12, 2014 at 22:10
  • 1
    $\begingroup$ You do not need double lines, $|x\cap y|$ is ok. $\endgroup$
    – Jimmy R.
    Nov 12, 2014 at 22:10
  • 1
    $\begingroup$ Yes. Except that the notation $\|\cdot\|$ usually is for norms. I think $|x|$ is more common to denote the cardinal of $x$. $\endgroup$
    – xavierm02
    Nov 12, 2014 at 22:11
  • 1
    $\begingroup$ This property is also often written as: $ \forall x\in X\; \forall y\in Y:\; x\cap y\ne\emptyset $ $\endgroup$
    – Danny
    Nov 12, 2014 at 22:14
  • $\begingroup$ Thanks everybody! Good to know about single vs double lines and the alternate version by Danny. $\endgroup$
    – dana
    Nov 12, 2014 at 23:13

0

Reset to default

You must log in to answer this question.

Browse other questions tagged .