On the set `C` of all complex numbers an operation `'o'` is defined by `z_1\ o\ z_2=sqrt(z_1z_2)` for all `z_1,\ z_2 in C` . Is `o` a binary operation on `C` ?

On the set C of all complex numbers an operation o' is defined by z_(1) o z_(2)=sqrt(z_(1)z_(2)) for all z_(1),z_(2)in C. Is o a binary operation on C?

On the set Z of all integers a binary operation * is defined by a*b=a+b+2 for all a,b in Z. Write the inverse of 4.

Determine whether O on Z defined by aOb=a^(b) for all a,b in Z define a binary operation on the given set or not:

On the set Z of integers a binary operation * is defined by a*b=ab+1 for all a,b in Z Prove that * is not associative on Z

Let A,B,C be three sets of complex numbers as defined below.A={z:|z+1| =1} and C={z:|(z-1)/(z+1)|>=1}

Construct the composition table for the composition of functions (o) defined on the S={f_1,\ f_2,\ f_3,\ f_4} of four functions from C (the set of all complex numbers) to itself, defined by f_1(z)=z ,\ \ f_2(z)=-z ,\ \ f_3(z)=1/z ,\ \ f_4(z)=-1/z for all z in Cdot

Is * defined by a^(*)b=(a+b)/(2) is binary operation on Z.