GATE | GATE CS 1997 | Question 16

Let (Z, *) be an algebraic structure where Z is the set of integers and the operation ∗ is defined by n ∗ m = max(n . m). Which of the following statements is true for (Z, *) ?
(A) (Z, *) is a monoid
(B) (Z, *) is an Abelian group
(C) (Z, *) is a group
(D) None of the above

Answer: (D)

Explanation: The given algebraic structure does not have an identity element since it is defined on the set of Integers and there is no minimum element in the set of integers.
Since it does not have an identity element, it is not a Monoid and consequently not a Group or Abelian Group.
Option D is therefore correct.

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