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.

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

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.

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

Let * be a binary operation on N defined by a*b= 2^(5ab),a b inN .Discuss the commutativity if this binary operation.

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

Prove that the binary operation o defined by a o b = |a|+|b|, AA a,b in R is commutative and associatie on R.

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

Let P(A) be the power set of a non-empty set A and a binary operation @ on P(A) is defined by X@Y=XcupY for all YinP(A). Prove that, the binary operation @ is commutative as well as associative on P(A). Find the identity element w.r.t. binary operation @ on P(A). Also prove that Phi inP(A) is the only invertible element in P(A).

Let * be a binary operations on Z and is defined by , a * b = a + b + 1, a, bin Z . Find the identity element.