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 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 if a binary operation * is defined by a*b= (a b)/5 , prove that * is associative on Qdot

Let a mapping '*' from Q xx Q to Q (set of all rational numbers) be defined by a* b = a +2 b for all a, b in Q. Prove 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)/5 for all a , b in Qdot Find the identity element for * in Q. Also, prove that every non-zero element of Q is invertible.

On Q, the set of all rational numbers, a binary operation * is defined by a*b=(a b)/5 for all a , b in Qdot 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 if the binary operation * is defined by a * b = 1/4ab for all a,b in Q^+ find the identity element in Q^+ .

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

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.