Questions & Answers

Question

Answers

(a) 1

(b) -1

(c) 0

(d) none

Answer
Verified

Given that we need to find the identity element with respect to addition in integers.

We know that an integer which is subjected to any addition operation to another integer to leave the value of another integer unchanged is known as the identity element with respect to addition.

Let us assume the identity element be ‘I’ and an element to represent integers be ‘Z’.

Since, ‘I’ is an identity element it should satisfy I + Z = Z + I = Z.

Let us start solving for I by using I + Z = Z.

So, we have got I + Z = Z.

We have got I = Z – Z.

We have got I = 0 ---(1).

Now, we start solving for I by using Z + I = Z.

So, we have got Z + I = Z.

We have got I = Z – Z.

We have got I = 0 ---(2).

From equations (1) and (2), we have got the value of the identity element when addition with integer is done as 0.

∴ The identity element with respect to addition in integers is 0.