Question

The identity element of subtraction is

Answer 1

Hint: We first define the algebraic expression for the subtraction of the two arbitrary numbers as $a-b$. Then we find the identity element of subtraction for which the input and output for the operation remain the same. We also show the concept of identity element for addition, multiplication and division.

Complete step by step solution:
The subtraction of any two arbitrary numbers a and b will be denoted by $a-b$.
Now the identity element is such a number for which the subtraction gives the same output as the input after the operation.
This means if we subtract $x$ from a, we get a back as the solution.
Therefore, $a-x=a\Rightarrow x=a-a=0$.
We get that the identity element of subtraction is 0.
So, the correct answer is “0”.

Note: We need to keep in mind the subtraction is a particular binary operation. The concept of identity element is fixed for all kinds of operations, be it multiplication or addition.
The identity element for the addition is also 0. For addition of a and b we express it as $a+b$.
This means if we add $x$ to a, we get a back as the solution.
$\begin{align}
  & a+x=a \\
 & \Rightarrow x=a-a=0 \\
\end{align}$
For multiplication and division, we get 1 as the identity element.
$\begin{align}
  & a\times x=a \\
 & \Rightarrow x=\dfrac{a}{a}=1 \\
\end{align}$
$\begin{align}
  & \dfrac{a}{x}=a \\
 & \Rightarrow x=\dfrac{a}{a}=1 \\
\end{align}$