Identity of the binary operation subtraction is 0

True

No worries! We‘ve got your back. Try BYJU‘S free classes today!

False

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is B
False

The binary operation subtraction(a,b) is equal to a-b. So, if e is the identity of subtraction, then a-e = a = e-a

by using the first relation(a-e = a), we get e = 0. Is this the identity of subtraction?

e = 0 does not satisfy the second relation a = e-a. If e =0, we get a=-a, which is not correct. So, where did we go wrong?

We started with an assumption that e is the identity of the subtraction. But we found that this is not true. Subtraction does not have identity.

Suggest Corrections

Similar questions

Identity of the binary operation subtraction is 0

Binary operation 'subtraction' on integers is

Q. Which of the following is true?
(a) * defined by

a * b = \frac{a + b}{2}

is a binary operation on Z
(b) * defined by

a * b = \frac{a + b}{2}

is a binary operation on Q
(c) all binary commutative operations are associative
(d) subtraction is a binary operation on N

Show that subtraction are not binary operation on natural number N

Let S = Z x (Z - {0}) and the binary operation * is defined as (a , b) * (c ,d) = (ad + bc , bd) for all a,b,c,d ϵZ. The identity element of of S for the binary operation * on S is __

Join BYJU'S Learning Program