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,