sets and sets notations

1. A set is a collection of elements, often
numbers, which can be indicated by
listing these elements in braces {}.
For example,
The set of whole numbers less than 7
is {1, 2, 3, 4, 5, 6}

2. Some sets have an infinite number
of elements, such as the set of all
set of all integers greater than -2:
{-1, 0, 1, 2, 3,…}

3. • A set containing no elements is called
the empty set, or null set, and is
indicated by the symbol Ø or { }.
• The set that contains all objects is
called the universal set or the
universe, usually labeled U.

4. • Any set is a subset of the universe.
• If a set is called A, then the
complement of A, written A’, is every
element in the universe U that is not
in A.

5. • The intersection of two sets is the set containing all
the elements in common to the two sets. An intersection
of sets is denoted by the symbol  between the set
names.
• Disjoint sets are sets that have no elements in
common, so their intersection is the empty set.

6. • The union of two sets is the set of
elements in one set or the other
set. The symbol for this operation
is .

7. Exercises
1)Given
A = {3, 4, 5, 6} and
B = {3, 6, 9, 12},
find A  B and A  B.

8. 2) Let C = {-4, -2, 0, 2} and
D = {1, 2, 3}, be two sets in universe
U = {-4, -3, -2, -1, 0, 1, 2, 3, 4}.
Find C’ and D’.

10. • The cross product or Cartesian product of
two sets A and B, denoted as A x B, is the set of
all ordered pairs (a, b) where a is an element of
A and b is an element of B.
Note that B x A is not the same as A x B and will
not be equal to it unless A = B or one of the two
sets is the empty set.

11. Given that A = {3, 4, 5} and
B = {1, 2, 3},
find A x B and B x A.

12. A Venn Diagram is useful for sorting and
classifying sets of objects or numbers.
Each circle in a Venn diagram represents
a subset of objects within the universal set
(represented by the rectangle). The
overlapping regions indicate objects that
the subset have in common. An object that
does not belong to a subset appears
outside the circles.

13. Example 1
The Venn diagram shows how many
students in a tenth grade class are
taking Spanish, French, and
Mandarin.
• How many students are studying
Spanish?
• How many are studying only
French?
• How many are studying both
Spanish and Mandarin?
• How many are studying Spanish,
French and Mandarin?

14. Example 2
In the Venn diagram at the right, the
universal set is {1, 2, 3, …9}
• What is the intersection of sets A
and B?
• What is the intersection of sets A,
B, and C?
• What is the intersection of sets A
and C?
• What is the union of sets B and C?

15. Example 3
Sets A and B are both in
universe U but are not
equal. Therefore, they are
either Disjoint Sets
(having no elements in
common) or overlapping
sets. Neither is a subset of
the other.