On Z, define `ox` by `(m ox n) = m^(n) + n^(m) : AA m, n in Z`. Is `ox` binary on Z?

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.

Is the binary operation * defined on Z (set of integers) by m**n=m-n +mn, AA m, n in Z commutative?

In equation (Z - 1)^(n) = Z^(n) = 1 (AA n in N) has solution, then n can be

Is the binary operation defined on Z . (set of integers) by m* n=m-n+mn, AA m,n in z commutative?

Is the binary operation'*' defined on Z (set of integers) by m*n = m-n + mn for all m,n in Z commutative?

Is the binary operation '*' defined on Z (set of integers) by the rule m*n = m - n for all m , n in Z commutative?

Let f : Z rarr Z be a function defined by f(n) =3n AA n in Z and g: Z rarrZ be defined by g(n) = {{:((n)/(3),"if n is a multiple of 3"),(""0, "if n is not a multiple of 3"):} Show that gof = I_(z) and fog ne I_(z) .

Let f : Z rarr Z be defined as f(n) = 3n for all n in Z . Let g : Z rarr Z be defined as g(n)= n/3 if n is a multiple of 3. g(n)= 0 if n is not a multiple of 3. Show that gof = I_z and fog ne I_Z

A function f is defined by f(x)=|x|^(m)|x-1|^(n)AA x in R. The local maximum value of the function is (m,n in N),1( b) m^(n)n^(m)(m^(m)n)/((m+n)^(m+n))(d)((mn)^(m+n))/((m+n)^(m+n))