Basically I'm trying to revise for my thursday exam and it's going terribly. I am struggling with these two questions....

Let X, Y be the permutations:...

X = (1 2 3 4 5 6 7) and $\displaystyle Y = (1234)(24756)$

----(1 5 7 4 6 2 3)

Write X, Y, X^3, XY as products of disjoint cycles and determine orders plus signs!

I really need a 'dummies' guide so to speak to this one. And X is written exactly like that with the numbers above and below.

__________________________________________________ ___________

The next question is:

Let f: Z5 -> Z5 be given by $\displaystyle f(x) = x^2$ - draw the diagram of f and determine wether its injective or surjective. Justify.

part ii) Give an example of a three element subset A -> Z5 such that the restriction of f to A is injective.

part iii) give an example of subsets B,C such that f takes each element of B to B and the resulting map $\displaystyle B->C$ is surjective.

These are the two questions I am currently stuck on, if anyone can offer advice to either one I reserve alot of thanks for you. I'm pretty sure I might need help on other questions but not until I have figured these out. Thanks alot in advance.