Let * be a binary operation on N,defined bya*b=`a^b,a,binN`.is * associative or commutative?

Let* be the binary operation on N given by a*b=LCM of a and b,Is * associative?

Let ast be a binary operation on N defined by aastb=HCF of a and b Is ast associative?

Let * be a binary operation on N , the set of all natural numbers defined by a * b = a^b , a, b in N . Is (N,*) associative or commutative?

Let ast be a binary operation on N defined by aastb=HCF of a and b Is ast commutative?

*be a binary operation on Q,defined as a**b=(3ab)/5 .Show that * is associative.

* be a binary operation on Q,defined as a**b=(3ab)/5 .Show that *is commutative.

Let ** ' be the binary operation on N given by a**'b = L.c.m. of a and b. Is ** associative ?

ast ' be a binary operation on NxxN defined as (a,b)ast(c,d)=(ac,bd) Show that ast is commutative.

Let A=NxN and '*' be a binary operation on A defined by (a,b)*(c,d)=(a+c,b+d) .Prove that '*' is commutative.

Let ** ' be the binary operation on N given by a**'b = L.c.m. of a and b. Is ** commutative ?