Section 2.2: Venn Diagrams and Subsets
The set of all possible elements in a problem is called the
universal set and is usually designated with the letter U.
Knowing what the universal set is for a problem will be
important:
Example. Use the listing method to list all of the
elements in the set A of even numbers, when the
universal set is as stated below.
(a) U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(b) U = {1, 2, 3, 4}
Venn Diagrams
Example. Use a Venn diagram to illustrate the universal
set U and the set A of even numbers, when the universal
set is as stated below.
(a) U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(b) U = {1, 2, 3, 4}
Complement of a Set
The complement of A, read as “A prime”, contains all
elements that are contained in U but are not in A.
Example. Use the listing method to list all of the
elements in the complement of the set A of even
numbers, when the universal set is as stated below.
(a) U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(b) U = {1, 2, 3, 4}
Subsets of a Set
Recall: in 2.1 we learned that Set A is a subset of set B if
every element of A is also an element of B. This is
written as 𝐴 ⊆ 𝐵.
Example. Let U = {l, m, n, o, p, q, r, s, t}, A = {q, r, s}
and B = {p, q, r, s, t}.
(a) Is the statement 𝐴 ⊆ 𝐵 true or false?
(b) Use a Venn diagram to illustrate sets A, B, and U.
(c) List the elements in A’.