On the set $Q^{+}$ of all positive rational numbers, define an operation $*$ on $Q^{+}$ by $a*b=\frac{ab}{2}$ for all $a, b \in Q^{+}$. Show that $*$ is commutative

On the set $Q^{+}$ of all positive rational numbers, define an operation $*$ on $Q^{+}$ by $a*b=\frac{ab}{2}$ for all $a, b \in Q^{+}$. Show that $*$ is associative.

Let $Q^{+}$ be the set of all positive rational numbers. Show that the operation $*$on $Q^{+}$ defined by $a*b=\frac{1}{2}(a+b)$ is a binary operation.

Let $Q^{+}$ be the set of all positive rational numbers. The operation $*$on $Q^{+}$ defined by $a*b=\frac{1}{2}(a+b)$ is a binary operation. Show that $*$ is commutative.

Let $Q^{+}$ be the set of all positive rational numbers. The operation $*$on $Q^{+}$ defined by $a*b=\frac{1}{2}(a+b)$ is a binary operation. Show that $*$ is not associative.

Let $Q$ be the set of all rational numbers. Define an operation on $Q–\{-1\}$ by $a*b=a+b+ab$. Show that  $*$ is a binary operation on $Q–\{-1\}$.

Let $Q$ be the set of all rational numbers. Define an operation $*$ on $Q-\left\{-1\right\}$ by $a*b=a+b+a b$. Show that $*$ is commutative.

Let $Q$ be the set of all rational numbers. Define an operation $*$ on $Q-\left\{-1\right\}$ by $a*b=a+b+a b$. Show that $*$ is associative.

Let $Q$ be the set of all rational numbers, an operation $*$ defined on $Q-\left\{-1\right\}$ by $a+b=a+b+a b$. Show that zero is the identity element in $Q-\left\{-1\right\}$  for $*$.