Each of the following involves a vector space V and a subset W. For each decide whether W is a subspace of V.

1.) V = R^{3}, W={(x,y,z) | x <= z } I say no because it doesn't preserve scalar multiplication. For example, if you have (2,2,4) 2 is <=4 but -2 >= -4 which contradicts that x must be less than or equal to z. Am I right?

2.) V = R_{<= 3}[x], W = Z_{<= 3}[x]. So V is the polynomials in x with real coefficients and degree at most 3. W is the polynomials in x with integer coefficients and degree at most 3. I'm not sure on this one, any help?