Vector Subspace of the Vector Space

1. Determine whether the following sets W are vector subspaces of the
vector space V.
a. V=R^4, A and B are two 3 X 4 matrices.
W={X is an element of R^4:Ax-3Bx=0}.
b. V=C',   W={f is an element of C': f(x+3)=f(x)+5
c. V=P,    W={f is an element of P: f'(2)=0}
d. V=C',   W={f is an element of C': The integral of f(x)dx from 0 to
3 = 2f(3)

I understand how to verify a vector subspace of a vector space, if it is closed under addition and scaler multiplication.  I am having trouble understanding and handling the notation.  Not sure which way to go.