let `**` be a binary on `QQ`, defined by
`a**b=(a-b)^(2)` for all `a,binQQ`. Show that the binary operation `**` on `QQ` is commutative but not associative.

Show that the binary operation ** defined on RR by a**b=ab+2 is commutative but not associative.

A binary operation ** on QQ , the set of rational numbers, is defined by a**b=(a-b)/(3) fo rall a,binQQ . Show that the binary opearation ** is neither commutative nor associative on QQ .

Let * be a binary operation defined by a* b = L.C.M , (a,b) AA a,b in N . Show that the binary operation * defined on N is commutative and associative. Also find its identity element of N.

let ** be a binary operation on RR , the set of real numbers, defined by a@b=sqrt(a^(2)+b^(2)) for all a,binRR . Prove that the binary operation @ is commutative as well as associative.

Let * be a binary operation on Zdefined by a*b=a+b- 15 for a,binZ . Show that *is commutative

Let * be a binary operation on Zdefined by a*b=a+b- 15 for a,binZ .Show that *is associative

An operation ** on ZZ , the set of integers, is defined as, a**b=a-b+ab for all a,binZZ . Prove that ** is a binary operation on ZZ which is neither commutative nor associative.

(I) Let ** be a binary operation defined by a**b=2a+b-3. Find 3**4. (ii) let ** be a binary operation on RR-{-1} , defined by a**b=(1)/(b+1) for all a,binRR-{-1} Show that ** is neither commutative nor associative. (iii) Let ** be a binary operation on the set QQ of all raional numbers, defined as a**b=(2a-b^(2)) for all a,binQQ . Find 3**5 and 5**3 . Is 3**5=5**3?

The binary operation * define on N by a*b = a+b+ab for all a,binN is

Prove that the operation @ on QQ defined by x@y=(x-2)/(y-2) for all x,yinQQ does not represent a binary operation on QQ .