Let `S` be the set of all rational number except 1 and * be defined on `S` by `a*b=a+b-a b ,` for all `a ,bSdot` Prove that (i) * is a binary operation on `( i i ) * is commutative as well as associative.

Let S be the set of all rational number except 1 and * be defined on S by a * b=a+b-a b , for all a ,bSdot Prove that (i) * is a binary operation on S ( i i ) * is commutative as well as associative.

If S is the set of all rational numbers except 1 and * be defined on S by a**b =a+b-ab , for all a, b in S . Prove that (i) * is a binary operation on S. (ii) * is commutative as well as associative.

If S is a set of all rational numbers except 1 and ** be defined on S by a ** b = a + b-ab for all a, b in s then prove that ** is a binary operation.

Let S be the set of all rational numbers except 1 and * be defined on S by a*b=a+b-a b , for all a , b in Sdot Find its identity element

Let S be the set of all rational numbers except 1 and * be defined on S by a*b=a+b-ab, for alla ,b in S. Find its identity element

Let S be the set of all real numbers except 1 and 'o' be an operation on S defined by : aob = a+b - ab for all a,b in S. Prove that S is closed under given operation.

If S is a set of all rational numbers except 1 and ** be defined on S by a ** b = a + b-ab for all a, b in s then prove that ** is commutative as well as associative.

Let S be the set of all real numbers except -1 and let * be an operation defined by a*b=a+b+ab for all a,b in S. Determine whether * is a binary operation on S. If yes, check its commutativity and associativity.Also, solve the equation (2*x)*3=7

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 S be the set of all real numbers except 1 and 'o' be an operation on S defined by : aob = a+b - ab for all a,b in S. Prove that the given operation is : (I) commutative (II) associative.