JEE MATHEMATICS MCQ: RELATIONS

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In the set

{N}

of natural numbers, define the binary operation

*

m * {n}=\operatorname{GCD}({m}, {n}), {m}, {n} \in {N}

. Then, which of the following is true?

I.

*

is not a binary operation

II.

*

is a binary operation

III. Inverse of each element of

{N}

exist

IV. Inverse of each element of

{N}

does not exist

View answer and explanation

Correct option: D

II and IV are true

Option D (II and IV are true) is correct because the GCD is a binary operation, and not all elements have an inverse under this operation.

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