Properties of Union and Intersection
Union and intersection are commutative and associative, and each distributes over the other: .
Proposition 2.5
We have a few properties about intersections and unions.
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we can view intersection as a special case of subset selection:
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intersection and union are commutative and associative:
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union is distributive over intersection, i.e.
and intersection is distributive over union:
Proof technique
Rewrite each identity between sets into a statement about an arbitrary element joined by inclusion and logical connectives, and settle the connectives with a truth table. Usually one shows both and .
Related
Stated in
- Proposition 2.5§2.1.2 Properties of Sets