Let $X$ be a non-empty compact Hausdorff space. Which of the following statements are true?
$a.$ If $X$ has at least $n$ distinct points, then the dimension of $C(X)$, the space of continuous real valued functions defined on $X$, is at least $n$.
$b.$ If $A$ and $B$ are disjoint, non-empty and closed sets in $X$, there exists $f \in C(X)$ such that $f(x) = −3$ for all $x ∈ A$ and $f(x) = 4$ for all $x ∈ B.$
$c$. If $A ⊂ X$ is a closed and non-empty subset and if $g : A → R$ is a continuous function, then there exists $f ∈ C(X)$ such that $f(x) = g(x)$ for all $x ∈ A.$
I can conclude that part C is true....but not conclude about parts a and b.. Help needed!