Let an operation * be defined on mathbbQ+ by a * b = fracab2. Then sho | Mathematics II 2078

Mathematics II20785 marksGroups

Let an operation $*$ be defined on $\mathbb{Q}^+$ by $a * b = \frac{ab}{2}$ . Then show that $\mathbb{Q}^+$ forms a group. [5]

Let an operation $*$ be defined on $\mathbb{Q}^+$ by $a * b = \frac{ab}{2}$. Then show that $\mathbb{Q}^+$ forms a group. [5]

A non-empty set G with a binary operation ∗ is called a group if it satisfies the following four axioms: 1. Closure 2. Associativity 3. Existence of Identity 4. Existence of Inverse Here, the operation is defined on Q⁺ (the set of all positive rationals) as: $a b = \frac{ab}{2}$ --- Let

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Let an operation * be defined on mathbbQ+ by a * b = fracab2. Then show that mathbbQ+ forms a group.