Number of binary operations

Show that the total number of binary operation from set A to A is n^(n^(2)).

On Q, the set of all rational numbers a binary operation * is defined by a*b=(a+b)/(2) Show that * is not associative on Q.

On the set Q of all rational numbers if a binary operation * is defined by a*b=(ab)/(5), prove that * is associative on Q.

On the set Q^(+) of all positive rational numbers a binary operation * is defined by a*b=(ab)/(2) for all a,b in Q^(+). The inverse of 8 is (1)/(8) (b) (1)/(2)(cc)2(d)4

The set of netural numbers is closed under the binary operations of :

On Q,the set of all rational numbers,a binary operation * is defined by a*b=(ab)/(5) for all a,b in Q. Find the identity element for * in Q Also,prove that every non-zero element of Q is invertible.

Commutativity of binary operations

Associativity of binary operations

Distributivity of binary operations