I have to find which of these subsets are subspaces of

I know that for a subset to be a subspace of a given set, it can't be an empty set, it must be closed under addition and closed under scalar multiplication.

I can see that is going to be a subspace of because if is real, then a real number plus a real number will yield a real number. Also, a real number multiplied by a real number will yield a real number.

But I don't know how to prove it, nor how to analyse any of the others algebraically.

Thanks in advance,