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Inclusion

Definition 3.2.1   Let and be two sets. The set is called a subset of if the following property holds:

We denote this by .

Example 3.2.2   Let and . Then .

If is not a subset of , we denote . For example, the set is not a subset of the set .

Proposition 3.2.3   If , and are three sets, such that and , then .

Here too, we can prove the proposition either with truth tables (v.s. 3.14). Now we fix some set , sometimes called an universal set. We write for the set of all subsets of , called the power set of .

Example 3.2.4   Let . Then

Example 3.2.5   Consider the empty set . We have:
• ;
• ;
• ;

Next: Equality Up: Operations with sets Previous: Operations with sets   Contents
root 2002-06-10