Sumset Of Cantor Set

Probability

Let $\mathcal{C} + \mathcal{C}$ denote the sumset of theCantor set $\mathcal{C}$ . That is, $\mathcal{C} + \mathcal{C} = \{x+y \, : \, x, y \in \mathcal{C}\}.$ Which of the following statements is true about $\mathcal{C} + \mathcal{C}$ ?

\mathcal{C} + \mathcal{C}

strictly contains

[0,2]

\mathcal{C} + \mathcal{C}

equals

[0,2]

[0,2]

strictly contains

\mathcal{C} + \mathcal{C}