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
.

Figure 2:
Inclusion (subset).

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 .