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 `Qdot`

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 rational numbers an operation * is defined by a*b=1+ab. show that * is a binary operation on Q.

On the set Z of integers a binary operation * is defined by a*b=ab+1 for all a,b in Z Prove that * is not associative on Z

On Z, the set of all integers,a binary operation * is defined by a*b=a+3b-4 Prove that * is neither commutative nor associative on Z.

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.

Q,the set of all rational number,* is defined by a^(*)b=(a-b)/(2), show that * is no associative

Define a binary operation on a set.

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

Let Q be the set of all rational numbers and * be the binary operation , defined by a * b=a+ab for all a, b in Q. then ,

Let '**' be a binary operation on Q defined by : a**b=(2ab)/(3) . Show that '**' is commutative as well as associative.