Answer:
The false statement among the given options is:
"A natural number cannot be an integer."
Step-by-step explanation:
This statement is false because a natural number can indeed be an integer.
To understand why, let's define each term:
1. Natural numbers: These are the numbers we use for counting, such as 1, 2, 3, 4, and so on. They are positive whole numbers.
2. Integers: Integers include all natural numbers as well as their negatives and zero. So, integers include numbers like -3, -2, -1, 0, 1, 2, 3, and so on.
As you can see, natural numbers are a subset of integers because they are included in the set of integers. For example, the natural number 3 is also an integer because it can be represented as +3.
In summary:
- An irrational number is always a real number. (True)
- A natural number can be an integer. (True)
- A rational number cannot be an irrational number. (True)
- An integer will always be a rational number. (True)
Therefore, the false statement is: "A natural number cannot be an integer."