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Example Questions
Example Question #1 : Natural Numbers, Integers, And Real Numbers
Are the sets and
equal?
To determine if two sets are equal to each other it must be proven that each set contains the same elements.
Recall the following terminology,
Now, identify the elements in each set.
This means all integers are elements of .
Let ,
is the value
for all integers.
Therefore if the element in
is,
This means that all elements in will be divisible by two and thus be an even number therefore, 3 will never be an element in
.
Thus, it is concluded that
Example Question #2 : Natural Numbers, Integers, And Real Numbers
Are the sets and
equal?
To determine if two sets are equal to each other it must be proven that each set contains the same elements.
Recall the following terminology,
Now, identify the elements in each set.
This means all integers are elements of .
Let ,
is the value
for all integers.
Therefore if the element in
is,
Since four also belongs to this means that all elements in
will be the same as those in
.
Thus, it is concluded that
Example Question #1 : Natural Numbers, Integers, And Real Numbers
What is the correct expression of the relationships between the sets comprised of natural numbers, real numbers, and integers?
The natural numbers are defined as , the integers are defined as
, and the real numbers (
) are defined as the set of all non-complex numbers. As such,
is a subset of
, and
is a subset of
.
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