Difference between revisions of "Intersection (set theory)"
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==Properties== | ==Properties== | ||
*For any sets <math>A, B</math>, <math>A \cap B \subseteq A</math> and <math>A \cap B \subseteq B</math>. Thus <math>A \cap B = A</math> if and only if <math>A \subseteq B</math>. | *For any sets <math>A, B</math>, <math>A \cap B \subseteq A</math> and <math>A \cap B \subseteq B</math>. Thus <math>A \cap B = A</math> if and only if <math>A \subseteq B</math>. | ||
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==See also== | ==See also== | ||
* [[Subset]] | * [[Subset]] | ||
* [[Union]] | * [[Union]] | ||
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Revision as of 12:38, 12 January 2025
The intersection of two or more sets is the set of elements that are common to all of them. Thus, the intersection of the sets 
and 
is the set 
.
Intersection is denoted by the symbol 
, so the preceding example could be written 
. One can also use the symbol for intersection in the way one uses a capital sigma (
) for sums, i.e. 
is the intersection of the 
sets 
.
Properties
- For any sets
, 
and 
. Thus 
if and only if 
.
, 
and 
. Thus 
if and only if 
.See also
Stub
