Question

State true or false:
Every whole number is a natural number
(a) True
(B) False

Answer 1

Hint: We solve this problem by using the definitions of a whole numbers and natural numbers.
The counting numbers are called natural numbers. These numbers start at 1.
The set of counting numbers along with 0 are called whole numbers.
By using the above two definitions we check whether the given statement is correct or wrong.

Complete step by step answer:
We are given that every whole number is a natural number.
We know that the counting numbers are called the natural numbers. These numbers start at 1.
Let us assume that the natural numbers as \[\mathbb{N}\] then we get the set of natural numbers as
\[\Rightarrow \mathbb{N}=\left\{ 1,2,3,4,....... \right\}\]
Now, let us take the definition of the whole numbers
We know that the set of counting numbers along with 0 are called whole numbers.
Let us assume that the whole numbers as \[W\] then we get the set of whole numbers from the definition as
\[\begin{align}
  & \Rightarrow W=\mathbb{N}\cup \left\{ 0 \right\} \\
 & \Rightarrow W=\left\{ 0,1,2,3,4,..... \right\} \\
\end{align}\]
Here we can see that there is a number 0 in the whole numbers but not in the set of natural numbers.
Here, we can see that 0 is a whole number but not a natural number.
Therefore, we can conclude that the given statement that every whole number is a natural number is wrong or false.
So, option (b) is the correct answer.


Note:
Students may make mistakes by using the standard statement of a number system.
We have the statement that every natural number is a whole number but every whole number is not a natural number.
Here, we can see that it says every natural number is a whole number. This means that all-natural numbers lie in the set of whole numbers. Also, it says that every whole number is not a natural number. Students may get confused and take the statement in reverse order.