`**` be a binary operation on R defined by
`a"*"b = (a)/(4)+b/(7) , a,b inR`.
Show that `**` is not commutative and associative.

L A = NxxN and ** be the binary operation on A defined by (a,b) "*" (c,d) = (a+c,b+d) Show that ** is commutative and associative . Find the identity element for ** on A , if any.

A binary operation ** be defined on the set R by a**b = a+b +ab . Show that ** is commutative, and it is also Associative.

If ** be binary operation defined on R by a**b = 1 + ab, AA a,b in R . Then the operation ** is (i) Commutative but not associative. (ii) Associative but not commutative . (iii) Neither commutative nor associative . (iv) Both commutative and associative.

** be binary operation defined on a set R by a**b=a+b-(ab)^2 . Show that ** is commutative, but it is not associative. Find the identity element for ** .

On R - {-1}, a binary operation ** defined by a"*"b = a + b +ab then find a^(-1) .

** is a binary operation on the set Q. a"*"b = (2a+b)/4 then find 2"*"3 .

Let ** be the binary operation on N defined by a"*"b = H.C.F of a and b . Is ** commutative ? Is ** associative ? Does there exist identity for this binary operation on N ?

Number of binary operations on the set {a,b} are

Let ** be the binary operation on Q define a**b = a + ab . Is ** commutative ? Is ** associative ?