In the set of rational numbers `Q`, the binary operation 'O' is defined as follows `aob = a + b - ab,AA a, b in Q` Then, prove that(i) `aob = boa`.

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 ,

On the set of integers I, if a binary operation 'o' be defined as aob = a - b for every a, b in I , then :

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

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 if the binary operation * is defined by a * b = 1/4ab for all a,b in Q^+ find the identity element in 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

Let R be the set of real numbers and * be the binary operation defined on R as a*b= a+ b-ab AA a, b in R .Then, the identity element with respect to the binary operation * is

Prove that the binary operation O defined by a o b = a-b+ab, AA a,b in Q is not commutative and associative.

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.