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3.An operation $\displaystyle *$ on a set $\displaystyle A$ is said to be binary,if $\displaystyle x*y\in A$,for all $\displaystyle x,y\in A$, and it is said to be commutative if $\displaystyle x*y=y*x$ for all $\displaystyle x,y\in A$.Now if $\displaystyle A=\big\{a_{1},a_{2},a_{3},...,a_{n}\big\}$ then find the following

(i)Total number of binary operations on $\displaystyle A$

(ii)Total number of binary operations on $\displaystyle A$ such that $\displaystyle a_{i}*a_{j}\neq a_{i}*a_{k},if j\neq k$

(iii)Total number of binary operations on $\displaystyle A$ such that $\displaystyle a_{i}*a_{j}<a_{i}*a_{j+1},\forall i,j$