State true or false:
Every whole number is a natural number
(a) True
(B) False
Answer
635.7k+ views
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.
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.
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