# Set Theory : Natural Numbers, Integers, and Real Numbers

## Example Questions

### Example Question #1 : Natural Numbers, Integers, And Real Numbers

Are the sets  and  equal?

Explanation:

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?

Explanation:

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 #3 : 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?