A-1 Law and order: Cartesian product, power sets 499
A
B
A ∩ B
Fig. A.2. Venn diagram/Euler circles A ∩ B: the intersection A ∩ B of two sets A and B is the set of all
elements which are elements of the set A and the set B: A ∩ B := {x | x ∈ A ∧ x ∈ B}.
A
B
A ∪ B
Fig. A.3. Venn diagram/Euler circles A ∪ B: the union A ∪ B of two sets A and B is the set af all elements
which are in the set A or the set B: A ∪ B := {x | x ∈ A ∨ x ∈ B}.
A
B
A∆B
Fig. A.4. Venn diagram/Euler circles: the symmetric difference A∆B of two sets A and B is the set af all
elements which are either in set A or in set B: A∆B := {x | x ∈ A ˙
∨x ∈ B}.
A
B
A \ B
Fig. A.5. Venn diagram/Euler circles: the difference set A \ B of two sets A and B is the set af all elements
of A which are not in B: A \ B := {x | x ∈ A ∧ x ∈ B}.
A
B
A ∩ B
Fig. A.2. Venn diagram/Euler circles A ∩ B: the intersection A ∩ B of two sets A and B is the set of all
elements which are elements of the set A and the set B: A ∩ B := {x | x ∈ A ∧ x ∈ B}.
A
B
A ∪ B
Fig. A.3. Venn diagram/Euler circles A ∪ B: the union A ∪ B of two sets A and B is the set af all elements
which are in the set A or the set B: A ∪ B := {x | x ∈ A ∨ x ∈ B}.
A
B
A∆B
Fig. A.4. Venn diagram/Euler circles: the symmetric difference A∆B of two sets A and B is the set af all
elements which are either in set A or in set B: A∆B := {x | x ∈ A ˙
∨x ∈ B}.
A
B
A \ B
Fig. A.5. Venn diagram/Euler circles: the difference set A \ B of two sets A and B is the set af all elements
of A which are not in B: A \ B := {x | x ∈ A ∧ x ∈ B}.