Transcript Combining Signed Numbers

Relationships Between Sets
Intersection
Just like the intersection of two roads,
the intersection of two sets are the elements that
are members of both sets.
Intersection
Set A = { 1, 2, 3 }
set B = { 3, 4, 5 }
A  B  3
The empty set
Set A = { 1, 2, 3 }
set B = { 4, 5, 6 }
A B  
There is no element that is in both sets, so the
intersection is the empty set.
The empty set
The symbol for the empty set is the Greek letter Phi

Do not put it in brackets.
 is not empty. It is a set with one element –
the Greek letter Phi
Venn Diagrams
One way to graphically represent sets
is by using Venn diagrams.
John Venn (1834 – 1923), was a British
logician and philosopher who
introduced the Venn diagram, which
is used in many fields, including set
theory, probability, logic, statistics,
and computer science.
Courtesy of Wikipedia
Universal Set
To use a Venn diagram, you must first start with a
universal set, represented by U, which contains all
of the elements being considered in a problem.
In a problem about Chevys and Fords, the universal
set might be the set of all cars.
Venn Diagram
If U = {all cars} and F = {all Fords}, the Venn diagram
would look like this:
U
F
It’s easy to see that F is a proper subset of U. F  U
Venn Diagram
The complement of F is the set that consists of all of
the members of U that are not in F (the green area)
U
F
The complement of F is written F’.
The complement would be all cars that are NOT Fords.
Venn Diagram
If U = {all cars}, and F = {all Fords}, and C = {all Chevys}
the Venn diagram would look like this:
U
F
C
It’s easy to see that both F and C are subsets of U.
Disjoint Sets
In this case, the
sets are disjoint meaning that they
don’t overlap.
U
F
C
F C  
There are no cars that are both Fords and Chevys
- my neighbor sort of has one, but that’s a long story…
Intersection
R = {redheads}
G = {people with
green eyes}
U
R
R  G  {green-eyed redheads}
G
Vocabulary
Element
Subset
Union
Intersection
Empty set
Union
Two people get married (union)
and merge their
DVD collections…
Union
They sell all the duplicates on eBay.
The DVD’s that are left are
the union of their collections.
all of hers + all of his – dups
Union
Mathematically, we say that the number of elements
in the union of two finite sets is:
the number of elements in Set A (his DVD’s)
PLUS the number of elements in Set B (her DVD’s)
MINUS the number of elements in the intersection
of the sets (duplicates).
n  A  B  n  A  n  B – n  A B 
Union
Set A = { 1, 2, 3 }
Set B = { 3, 4, 5 }
A  B  1,2,3,4,5