Norm unit balls and sub spaces

Please see attached problems and explain all answers

Indicate which of the following are unit balls of valid norms in 32. 1' + Let S = C([0, 1]) (i.e., the space of bounded, continuous functions on [0, 1]). In the following, assume that U and ) are distinct non-empty subspaces of S. Which of the following are subspaces of S? Select all that apply.} fes : So f (t ) at = So tf (t)at V The intersection Un V {f E S : f is a polynomial of degree at most p} Of Es : So f (t ) dt = 1 {f Es : [f(t)|