Let $f\colon \mathbb R\rightarrow \mathbb R$ be a continuous function. Define $G = \{(x, f(x)) : x \in \mathbb R\} \subseteq \mathbb R^2$. Pick out the true statements:
a. $G$ is closed in $\mathbb R^2$.
b. $G$ is open in $\mathbb R^2$.
c. $G$ is connected in $\mathbb R^2$.
I think c is correct since $f$ is continuous but no idea about a and b.