A binary `@` on `NN` is defined by `a@b=L.C.M.(a,b)` for all `a,binNN.`
(i) Examine the commutativity and associativity of `@` on `NN`,
(ii) Find the identity element in `NN`,
(iii) Also find the invertible elements of `NN`.

A binary operation ** on NN is defined by a**b=L.C.M.(a,b) for all a,binNN . (i) Find 15**18 (ii) Show that ** is commutative as well as associative on NN. (iii) Find the the identity element in NN . (iv) Also find the invertible element in NN .

A binary operation @ is defined on RR-{-1} by a@b=a+b+ab for all a,binRR-{-1}. (i) Discuss the commutativity and associativity of @ on RR-{-1} . Find the identity element, if exists. (iii) Prove that every element of RR-{-1} is invertible.

Show that the operation ** on ZZ , the set of integers, defined by. a**b=a+b-2 for all a,b inZZ (i) is a binary operation: (ii) satisfies commutaitve and associative laws: (iii) Find the identity elemetn in ZZ , (iv) Also find the inverse of an element ainZZ.

Prove that the binary operation @ defined on QQ by a@b=a-b+ab for all a,b in QQ is neither commutative nor associative.

Let A=NNxxNNand@ be a binary operation on A defined by (a,b)@(c,d)=(ac,bd) for all a,b,c,dinNN . Discuss the commutativity and associativity of @ on A.

The binary operation ** defined on NN by a**b=a+b+ab for all a,binNN is--

Let ** be a binary on NN defined by a**b=L.C.M. (a,b) (for all a,bin NN) . 2**4=lambda then lambda will be---

Prove that the operaton ** on QQ-{1} given by a*b=a+b-ab for all a,binQQ-{1} (i) is closed: (ii) satisfies the commutative and associative laws, (iii) Find the identity element, (iv) Find the inverse of any element ainQQ-{1}.

Let ** a binary operation on NN given by a**b=H.C.F (a,b) for all a,binNN , write the value of 22**4

Prove that the binary operation ** on RR defined by a**b=a+b+ab for all a,binRR is commutative and associative.