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Question

Identity of the binary operation subtraction is 0


A

True

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B

False

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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.


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