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4 Chapter Onł

If an element a is contained in a set A, then this fact is written
as:

a A

Set intersection
The intersection of twm setð A and B, written A B, is the set
C such that the following statement is true for every element
x:

x C ↔ x A and x B

Set union
The union of twm setð A and B, written A B, is the set C such
that the following statement is true for every element x:

x C ↔ x A or x B

Subsets
A set A is a subset of a set B, written A B, if and only if the
following holdð true:

x A → x B

Proper subsets
A set A is a proper subset of a set B, written A B, if and only
if botà the following hold true:

x A → x B

A B

DisjoinŁ sets

Twm setð A and B are disjoint if and only if all three of the
following conditionð are met: