Download 3_5 Set Builder Notation - Miami Arts Charter School

3.5 SETS
Roster Form: use the { } to list the
elements of the set
ex: { 1, 2, 3, 4, 5, 6, 7, 8, 9}
Set Builder Notation: use the { } to
describe the properties of the elements
of the set
ex: { x | 1 < x < 9 }
Empty Set (Null Set): set that contains
no elements
ex: { },
Universal Set: the largest set we
are using
Ex:
{ x | x is an element of the real numbers}
Subset ( ): the list of some or all the
elements in a set.
Ex: A = { x |0 < x < 9 }
Some subsets are:
B = {1} C = {1,2} D = {1,2,3}
E = {1,2,3,4} ,,, etc.
Complement of a Set (A’): the set of all
elements in the universal set that are
not in the set .
Ex: A = { x |0 < x < 9 }
B = { x | multiple of 2 and < 9}
B’ = { 1, 3, 5, 7 }
GOAL:
REMENBER THE REAL NUMBERS
RATIONALS : Any number that can be written in
fraction form
3, 1/3, -5, -1/5, 1+(2/3), ….
INTEGERS: Naturals and Whole and Negative
numbers.
…-3,-2,-1,0,1,2,3,…..
WHOLE NUMBERS: Naturals
and 0
0,1,2,3,……
NATURAL NUMBERS:
Numbers we use to
count items.
1, 2, 3, 4,……..
IRRATIONALS:
Numbers that
cannot be
written in
fraction and
decimal
values do not
repeat.
π, √3,
REAL-WORLD:
Let the Universal set
U = {planet’s in Earth’s solar system}
and set
P = {planets farther from the sun than
earth is from the sun}. What is the
complement of
set P? Write
the answers in
both forms.
SOLUTION: Remember that the complement
of a set are the elements that are not on that
set.
U = { Mars, Jupiter, Saturn, Uranus, Neptune,
Mercury, Earth, Venus}
P = { Mars, Jupiter, Saturn, Uranus, Neptune}
COMPLEMENT (P’): Elements not in P
P’ = {Mercury, Earth, Venus}
YOU TRY IT:
Let
U = {days of the week}
A = { days of the week with letter N}
a) What are the elements of U?
b) What are the elements of A?
c) How do you find A’?
SOLUTION:
a)
U = { Sunday, Monday, Tuesday, Wednesday,
Thursday, Friday, Saturday}
b)
A = { Sunday, Monday, Wednesday}
c)
To find A’ we look for the elements that are
in U but not in A: { Tuesday, Thursday,
Friday, Saturday}
VIDEOS:
Sets
Sets of Numbers:
http://www.khanacademy.org/math/probability/in
dependent-dependentprobability/basic_set_operations/v/universal-setand-absolute-complement
http://www.khanacademy.org/math/probability/in
dependent-dependentprobability/basic_set_operations/v/relativecomplement-or-difference-between-sets
CLASSWORK:
Page 197-198:
Problems: 1, 3, 5,
6, 7, 10, 24
25, 30, 32, 47.