You've got the right idea, but it might be useful to use a bit different notation, since a recursion is asked for. Something like this for c) maybe:
Let be the set of positive multiples of 4.
I have some definitions that would apply to these, but I'm not sure whether or not they are very concrete, and I would also like to confirm that they are correct. Here are the sets and my current answers.
a) The set of odd positive numbers.
If , then
b) The positive integer powers of 3.
If , then
c) The positive multiples of 4.
If , then
Are these all accurate, or would they benefit from more detailed answers?