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 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.

Define a binary operation on a set.

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

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.

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

On the set W of all non-negative integers * is defined by a*b=a^(b) .Prove that * is not a binary operation on W.

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

Let Q^(+) be the set of all positive rational numbers (i) show theat the operation * on Q^(+) defined by a* b = 1/2 (a+b) is binary operation (ii) show that * is commutative (iii) show that * is not associative

If the operation * is defined on the set Q of all rational numbers by the rule a*b=(ab)/(3) for all a,b in Q. Show that * is associative on Q