I have a simple question, if we have two collection of sets, instead of sets, A and B, how is the intersection of A and B defined, is it defined as

{a intersection b:a a set in A and b a set in B}

thx

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- Sep 13th 2011, 12:57 PMsungunion of collections
I have a simple question, if we have two collection of sets, instead of sets, A and B, how is the intersection of A and B defined, is it defined as

{a intersection b:a a set in A and b a set in B}

thx - Sep 13th 2011, 01:11 PMPlatoRe: union of collections
- Sep 13th 2011, 01:24 PMsungRe: union of collections
$\displaystyle A \cap B$={$\displaystyle P \cap U$,$\displaystyle P \cap V$,...}

So can we define this as

$\displaystyle A \cap B$={$\displaystyle I_{1} \cap I_{2}$;for $\displaystyle I_{1} \in A$ and $\displaystyle I_{2} \in B$} - Sep 13th 2011, 01:29 PMPlatoRe: union of collections
- Sep 13th 2011, 01:41 PMsungRe: union of collections
yes is that the correct definition for the intersection of two collections?

So how is the intersection of two collections defined? - Sep 13th 2011, 02:04 PMPlatoRe: union of collections
I have no idea what you mean by that question.

This is a collection of sets $\displaystyle \{G\cap H:G\in\mathcal{A}\text{ and }H\in\mathcal{B}\}$

$\displaystyle J\in\mathcal{A}\cap\mathcal{B}\iff J\in\mathcal{A}\text{ and }J\in\mathcal{B}$.

$\displaystyle \bigcup\limits_{G \in A\;\& \;H \in B} {\left\{ {G \cap H} \right\}} $ is the set of**elements**which are in the intersection of a set in $\displaystyle \mathcal{A}$ and some set in $\displaystyle \mathcal{B}$. - Sep 13th 2011, 02:47 PMemakarovRe: union of collections
The definition of the intersection of two sets is the same regardless of the nature of the elements of those two sets: whether they are numbers, other sets, etc.

- Sep 13th 2011, 05:37 PMPlatoRe: union of collections