Consider a binary operation `""^(**)` on N defined by `a^(**)b=a^(3)+b^(3),a,b in N`, Examine, if
`""^(**)` is associative

Consider a binary operation ""^(**) on N defined by a^(**)b=a^(3)+b^(3),a,b in N , Examine, if ""^(**) is commutative

Consider the binary operation ""^(**) on N defined by a^(**)b="LCM" of a and b. Examine, if ""^(**) is associative

Consider the binary operation ""^(**) on N defined by a^(**)b="LCM" of a and b. Examine, if ""^(**) is commutative

Consider the ninary operation ""^(**) on N defined by a^(**)b="HCF" of a and b. Examine, if ""^(**) is associative

Consider the ninary operation ""^(**) on N defined by a^(**)b="HCF" of a and b. Examine, if ""^(**) is commutative

Consider the binary operations ""^(**):RxxRtoR and o:RxxR defined by a^(**)b=|a-b| aob=a, AA a,b in R Examine, if o distributes over ""^(**) .

Let ""^(**):QxxQtoQ is defined by a^(**)b=1+ab,AA a,b in Q . Show that ""^(**) is commutative, but not associative.

Let ""^(**) be a binary operation on Q, defined by a^(**)b=(3ab)/(5) . Show that ""^(**) is commutative, if it exists.