Maps in discrete scrutures?

Question

Write down all the values of the map
t : Z(15) --> Z(3) x Z(5), r ---> (u(3)r, u(5)r))

u(n) : Z --> Z(n), z |-->u(n)z

please vist http://www.sosmath.com/CBB/viewtopic.php?t=25706
for a better explaination

Answer 1

What, you mean the mapping from the ring of integers mod 15 to the cartesian product of the ring of integers mod 3 and the ring of integers mod 5, given by the residue mod 3 and mod 5, respectively? That would look something like this:

0→(0,0)
1→(1,1)
2→(2,2)
3→(0,3)
4→(1,4)
5→(2,0)
6→(0,1)
7→(1,2)
8→(2,3)
9→(0,4)
10→(1,0)
11→(2,1)
12→(0,2)
13→(1,3)
14→(2,4)