
Show that subtraction is not a binary operation on all natural numbers $N$.
Answer
411.6k+ views
Hint: In order to this question, to show whether the subtraction are not a binary operation on natural number $N$ , we will show the given statement by taking two natural number in which first number is smaller than the second number and when it will give the negative result, then it proves that subtraction are not binary operation on natural number $N$.
Complete step-by-step solution:
As we know that, the multiplication of natural numbers is also a natural number:
\[N \times N = N\]
Where, \[\left( {a,b} \right) = a - b\]
here a and b are natural numbers \[\left( {i.e.1,2,3,4,5,6,7,8,9...............} \right)\]
Now,
let \[a = 3\] and \[b = 5\]
\[a - b = 3 - 5\]
but since \[ - 2\] is not a natural number
\[\therefore \] Subtraction is not a binary operation on $N$ (natural number).
Note: The term "binary" refers to something that is made up of two parts. A binary operation is nothing more than a law for combining two values to produce a new one. The most well-known binary operations are addition, subtraction, multiplication, and division on different sets of numbers, which were taught in elementary school.
A binary operation on a set is a calculation that involves two set elements to generate another set element.
Natural numbers, which include all positive integers from 1 to infinity, are a part of the number system. Natural numbers, which do not contain zero or negative numbers, are also known as counting numbers. They are just positive integers, not zero, fractions, decimals, or negative ones, and they are a part of real numbers.
Complete step-by-step solution:
As we know that, the multiplication of natural numbers is also a natural number:
\[N \times N = N\]
Where, \[\left( {a,b} \right) = a - b\]
here a and b are natural numbers \[\left( {i.e.1,2,3,4,5,6,7,8,9...............} \right)\]
Now,
let \[a = 3\] and \[b = 5\]
\[a - b = 3 - 5\]
but since \[ - 2\] is not a natural number
\[\therefore \] Subtraction is not a binary operation on $N$ (natural number).
Note: The term "binary" refers to something that is made up of two parts. A binary operation is nothing more than a law for combining two values to produce a new one. The most well-known binary operations are addition, subtraction, multiplication, and division on different sets of numbers, which were taught in elementary school.
A binary operation on a set is a calculation that involves two set elements to generate another set element.
Natural numbers, which include all positive integers from 1 to infinity, are a part of the number system. Natural numbers, which do not contain zero or negative numbers, are also known as counting numbers. They are just positive integers, not zero, fractions, decimals, or negative ones, and they are a part of real numbers.
Recently Updated Pages
Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Write the following in Roman numerals 25819 class 7 maths CBSE

Trending doubts
Full Form of IASDMIPSIFSIRSPOLICE class 7 social science CBSE

Choose the correct assertive sentence form of the below class 7 english CBSE

Fill in the blanks with appropriate modals a Drivers class 7 english CBSE

What are the controls affecting the climate of Ind class 7 social science CBSE

The southernmost point of the Indian mainland is known class 7 social studies CBSE

Write a letter to the editor of the national daily class 7 english CBSE
