2.14  (I) Prove that an infinite set X is countable if and only if there is a sequence 
	of all the elements of X which has no repetitions. 

        (II) Prove that every subset S of a countable set X is itself countable.
        (III)  Prove that if

 there is a sequence  of all the elements of a set X, possibly 
	   with repetitions, then X is countable.
        (IV) If X is countable and is a surjection, prove that Y is countable.

2.15 Prove that if are countable sets, then is also countable.