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Example Questions
Example Question #5 : Irrational Numbers
Which of the following is an irrational number?
A rational number can be expressed as a fraction of integers, while an irrational number cannot.
can be written as
.
is simply
, which is a rational number.
The number can be rewritten as a fraction of whole numbers,
, which makes it a rational number.
is also a rational number because it is a ratio of whole numbers.
The number, , on the other hand, is irrational, since it has an irregular sequence of numbers (
...) that cannot be written as a fraction.
Example Question #1 : Number Sets
If ,
, and
, then find the following set:
The union is the set that contains all the numbers from and
. Therefore the union is
.
Example Question #2 : Number Sets
If ,
, and
, find the following set:
The intersection is the set that contains only the numbers found in all three sets. Therefore the intersection is .
Example Question #71 : Number Theory
If ,
, and
, find the following set:
The intersection is the set that contains the numbers that appear in both and
. Therefore the intersection is
.
Example Question #3 : Number Sets
If ,
, and
, find the following set:
The intersection is the set that contains the numbers found in both sets. Therefore the intersection is .
Example Question #5131 : Algebra Ii
If ,
, and
, find the following set:
The union is the set that contains all of the numbers found in all three sets. Therefore the union is . You do not need to re-write the numbers that appear more than once.
Example Question #82 : Number Theory
If ,
, and
, find the following set:
The intersection is the set that contains the numbers found in both sets. Therefore the intersection is .
Example Question #1 : Number Sets
Which set of numbers represents the union of E and F?
The union is the set of numbers that lie in set E or in set F.
.
In this problem set E contains terms , and set F contains terms
. Therefore, the union of these two sets is
.
Example Question #3442 : Algebra 1
Express the following in Set Builder Notation:
and stands for OR in Set Builder Notation
Example Question #1 : Number Sets
Find the intersection of the two sets:
To find the intersection of the two sets, , we must find the elements that are shared by both sets:
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