# Set theORY

• May 25th 2007, 05:42 PM
Singular
Set theORY
$\displaystyle \bigcap S$ denotes the set $\displaystyle \left\{ {x;\ \forall X \in S,x \in X} \right\}$
for any non-empty set S

And $\displaystyle \bigcup S$
denotes the set $\displaystyle \left\{ {x;\ \exists X \in S,x \in X} \right\}$
for any set S
Does anyone know how to explain waht it's mean?
Can it be explain using Venn Daigaram?
• May 25th 2007, 07:01 PM
Jhevon
Quote:

Originally Posted by Singular
$\displaystyle \bigcap S$ denotes the set $\displaystyle \left\{ {x;\ \forall X \in S,x \in X} \right\}$

Here we are considering a set S whose elements are sets. this symbol denotes the set of all elements that fall in the intersection of the sets contained in S. So any element that is in EVERY set in S will be in the set $\displaystyle \bigcap S$

Quote:

for any non-empty set S

And $\displaystyle \bigcup S$
denotes the set $\displaystyle \left\{ {x;\ \exists X \in S,x \in X} \right\}$
this again is talking about a set S whose elements are sets. any element that is in the union of all the sets will be in $\displaystyle \bigcup S$, that is any element that is in ANY set $\displaystyle X \in S$ will be in the set $\displaystyle \bigcup S$

Quote:

Can it be explain using Venn Daigaram?
I've never actually seen these represented using Venn Diagrams, but it may be possible. In the class I took we used a kind of number line approach