The following Venn diagram represents the relationship between whole numbers, integers, and rational numbers.
Based on the diagram, which of the following statements are true.
Select THREE correct answers.
All whole numbers are also integers.
All negative numbers are integers.
There are some rational numbers that are not integers.
A whole number is also a rational number.
All whole numbers are also integers - This statement is true because the circle for whole numbers is completely inside the circle for integers.
All negative numbers are integers - This statement is true because the circle for negative numbers is completely inside the circle for integers.
There are some rational numbers that are not integers - This statement is true because the circle for rational numbers extends beyond the circle for integers.
A whole number is also a rational number - This statement is true because the circle for whole numbers is completely inside the circle for rational numbers.
Based on the Venn diagram, the correct statements are:
1. All whole numbers are also integers.
2. All negative numbers are integers.
3. There are some rational numbers that are not integers.
Therefore, the three correct statements are:
1. All whole numbers are also integers.
2. All negative numbers are integers.
3. There are some rational numbers that are not integers.
To determine which of the statements are true based on the Venn diagram, we need to understand the relationships between the different number sets.
The Venn diagram consists of three overlapping circles representing whole numbers, integers, and rational numbers. Let's analyze each statement:
1. All whole numbers are also integers: True
If we look at the diagram, we can see that the circle representing whole numbers is entirely contained within the circle representing integers. This means that every whole number is also an integer.
2. All negative numbers are integers: True
In the diagram, the circle representing integers contains both positive and negative numbers. Therefore, all negative numbers are integers.
3. There are some rational numbers that are not integers: True
In the diagram, the circle representing rational numbers extends beyond the circle representing integers. This implies that there are rational numbers that are not integers, such as fractions or decimals that are not whole numbers.
4. A whole number is also a rational number: True
Since the circle representing whole numbers is entirely contained within the circle representing rational numbers, we can conclude that every whole number is also a rational number.
Therefore, the correct statements are:
- All whole numbers are also integers.
- All negative numbers are integers.
- There are some rational numbers that are not integers.