Problems
Problem :
Let set
A = {1, 2, 3}
and set
B = {4, 5}
. What is their Cartesian
product
A×B
?
A×B = {(1, 4),(1, 5),(2, 4),(2, 5),(3, 4),(3, 5)}
. This is every
possible ordered pair from which the first element is taken from
A
and the
second element taken from
B
.
Problem :
What is the Cartesian product of the set of real numbers and itself?
The Cartesian product is every ordered pair in the coordinate plane.
Problem :
What is the Cartesian product of the set of positive real numbers with itself?
The Cartesian product is every ordered pair in the first
quadrant of the coordinate plane.
Problem :
What is the domain and range of the relation
{(2, 4),(4, 8),(8, 16)}
?
Domain
D = {2, 4, 8}
. Range
R = {4, 8, 16}
.
Problem :
What is the domain and range of the relation
y = ±
?
Domain
D
is real numbers
> 0
. Range
R
is all real numbers.