Transcript Course 3 Lesson 90

Lesson 90 Warm Up
• Pg. 599
Course 3
Lesson 90
Sets
Sets
• A set is a collections of elements.
• Almost anything can be an element, for
example, numbers, ordered pairs, variables, or
geometric figures.
• The elements of a set are often listed in braces, {
}.
• The set of whole numbers can be expressed this
way: {0, 1, 2, 3, …}
• The ellipsis (…) indicates that the elements of the
set continue in the same pattern without end.
The set of integers can be expressed this way:
{…, -3, -2, -1, 0, 1, 2, 3, …}
Example 1
• Use set notation to denote the set of even
integers.
Elements/Example 2
• To indicate an element of a set use a
symbol like a curved E.
3 ε{integers}
½ ε{integers}
• Use set notation to indicate whether each
number is an element of the set of rational
numbers.
a. 2
b. ½
c. √2
Example 3
Subsets
U
• Sets can be related to each other in various
ways. If all of set A is contained in set B, then
set A is a subset of set B. The subset symbol is
similar to a U rotated 90° clockwise.
A B
“A is a subset of B”
• For example, the set of rectangles is a subset
of the set of quadrilaterals, because every
rectangle is a quadrilateral.
rectangles quadrilaterals
U
Symbols
•
•
•
•
Natural (counting) numbers
Integers
Rational numbers (quotients)
Real Numbers
Example 4
Venn diagrams
• We can use Venn diagrams to illustrate the
relationships among sets. This diagram shows
that the set S (squares) is a subset of set R
(rectangles).
Set S
Set R
Intersections/Unions
• Sets A and B overlap if some elements of set
A are also elements of set B. The region is
called the intersection of sets A and B and is
shown with the symbol .
• Unions combine the elements from both
sets.
Rectangles
Rhombuses
U
Squares
Example 5
Set Notation Symbols
U
{ } The set of
ε is an element of
is a subset of
The intersection of
U The union of
Ø Empty set
U
Example 6
Lesson 90 Homework
• Pg. 602 Practice, WS #90