Provide a recursive definition of the following sets

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.

$\displaystyle 1\in S$

If $\displaystyle x\in S$, then $\displaystyle x+2\in S$

**b)** The positive integer powers of 3.

$\displaystyle 3\in S$

If $\displaystyle x\in S$, then $\displaystyle 3\times x\in S$

**c)** The positive multiples of 4.

$\displaystyle 4\in S$

If $\displaystyle x\in S, y\in S$, then $\displaystyle x+y\in S$

Are these all accurate, or would they benefit from more detailed answers?