i am reviewing for topology exam coming up and i was wondering if somebody can show me how to do some review questions

prove following statements about continuous functions and discrete and indiscrete topologies

1. if X is discrete, then every function f from X to a topological space Y is continuous.

2. if X is not discrete, then there is a topological space Y and a function f:X->Y that is not continuous. (hint: let Y be the set X with discrete topology)

3. if Y is a n indiscrete topological space, then every function f from a topological space X to Y is continuous.

4. if Y is not indiscrete, then there is a topological space X and a function f:X->Y that is not continuous.

thank you for any help!