Binary Operations

The binary operation $*R\times R\to R,$ is defined as  $a*b=2a+b.$ From the given options choose the value of  $\left(2*3\right)*4$ is equal to

Let $\odot$ be a binary opertation on $\mathrm{\mathbb{Q}}-\left\{0\right\}$ defined by a $\odot b=\frac{a}{b}$. Then $1\odot \left(2\odot \left(3\odot 4\right)\right)$ is equal to

Show that division is not a binary operation on real numbers$\left(R\right)$. Give one example.

Show that subtraction and division are not binary operations on $N$.

$a*b$ is a binary operation, $a=b$. Verify reflexive property for given binary operation.

$a*b$ is a binary operation, $a<b$. Verify reflexive property for given binary operation.

$a*b$ is a binary operation, $a\le b$. Verify reflexive property for given binary operation.

$a*b$ is a binary operation, $a\ge b$. Verify reflexive property for given binary operation.

$a*b$ is a binary operation, $a>b$. Verify reflexive property for given binary operation.

Suppose $*$ be the multiplication operation and $\#$ be the addition operation defined on $Z$. Let $a=10,b=11 \text{and} c=12$, then find $a*(b\#c)$.

Suppose $*$ be the multiplication operation and $\#$ be the addition operation defined on $Z$. Let $a=5,b=6 \text{and} c=8$, then find $a*(b\#c)$.

Suppose $*$ be the multiplication operation and $\#$ be the addition operation defined on $Z$. Let $a=3,b=4 \text{and} c=7$, then find $a*(b\#c)$.

Suppose $*$ be the multiplication operation and $\#$ be the subtraction operation defined on $Z$. Let $a=5,b=6 \text{and} c=8$, then find $a*(b\#c)$.

Suppose $*$ be the multiplication operation and $\#$ be the subtraction operation defined on $Z$. Let $a=3,b=4 \text{and} c=7$, then find $a*(b\#c)$.

If $a*b=\frac{ab}{10};a,b\in Q^{+}$, then ${\left(5*8\right)}^{-1}=\_\_\_\_\_\_\_\_$

Construct the composition table for ${\times }_{10}$ on set $S=\{1, 3, 7, 9\}$. 

Construct the composition table for ${\times }_5$ on set $Z_5=\{0, 1, 2, 3, 4\}$. 

Construct the composition table for ${\times }_6$ on set $S=\left\{0, 1, 2, 3, 4, 5\right\}$. 

Define binary operations on sets?

Let* be a binary operation on the set $R$ of real numbers defined by $a^{*}b=\frac{3ab}{7}$, then the identity element in $R$ for ${}^{*}$ is