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GO Classes 2023 | IIITH Mock Test 1 | Question: 5

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$(\text{Q}, \ast)$ is an algebraic structure where $\text{Q}$ represents rational numbers and $\ast$ denotes multiplication. Which one of the following statements is true?

  1. $\text{Q}$ is an abelian group.
  2. $\text{Q}$ is a group but not abelian.
  3. $\text{Q}$ is a semigroup but not a monoid.
  4. $\text{Q}$ is monoid but not group.
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1.closed since a*b belongs to ab

2.identity ,a*e=a

e=1

3.associative

since multiplication is associative ,associative property holds

4.inverse property

since 0 has no inverse

inverse property does not holds

hence,(Q,*) is monoid but not a group
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