Consider the vector space $\displaystyle \mathcal{F} = \lbrace f : \mathbb{R} \to \mathbb{R} \rbrace$.

(a) Let

$\displaystyle \mathcal{U} = \lbrace f : \mathbb{R} \to \mathbb{R} : f(3) = 0 \rbrace$

Prove true or show to be false: $\displaystyle \mathcal{U}$ is a subspace of $\displaystyle \mathcal{F}$.

(b) Let

$\displaystyle \mathcal{V} = \lbrace f : \mathbb{R} \to \mathbb{R} : f(3) = 3 \rbrace$

Prove true or show to be false: $\displaystyle \mathcal{V}$ is a subspace of $\displaystyle \mathcal{F}$.