Section 2.3 Notes Page 1
2.3 Venn Diagrams and Set Operations.
A universal set, symbolized by U, is a set that contains all the elements being considered in
given discussion or problem.
Venn diagrams, named for the British logician Jon Venn (1834 -1923), are used to show the
visual relationship among sets.
Four basic relationships;
1. Disjoint Sets: Two sets that have no elements in common
2. Proper Subsets: If set A is a Proper subset of setB
3. Equal Sets: The set A contains exactly the same elements as set B.
Section 2.3 Notes Page 2
4. Sets with some common elements: If set A and set B have at least one elementin common.
The complement of set A, symbolized by 𝐴′ , is the set of all elements in the universal set that
are not in A.
The intersection of sets A and B, written 𝐴 ∩ 𝐵, is the set of elements common to both set A
and set B.
The union of sets A and B, written 𝐴 ∪ 𝐵, is the set of elements that are members of set A or
of set B or of both sets.
Section 2.3 Notes Page 3
Ex1. Use the Venn diagram in figure to determine each of the following sets:
a) U
b) A
c) The set of elements in U that are not in A.
Ex2. Use the Venn diagram to determine each of the following sets:
a) U
b) B
c) The set of elements in A but not B
d) The set of elements in U that are not in B
e) The set of elements in both A and B.
Ex3. Given U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 7, 9}, and B = {3, 7, 8, 10}
Find each of the following sets:
a)
b)
c)
d)
e)
f)
g)
h)
i)
𝐴′
𝐴∩𝐵
𝐴∪𝐵
𝐴∩∅
𝐵∪∅
(𝐴 ∪ 𝐵)′
𝐴′ ∩ 𝐵 ′
𝐴 ∪ 𝐵′
(𝐴 ∩ 𝐵)′