Let $J_c$ be the Julia set for the quadratic polynomial $f_c(z) = z^2 + c$, and the Mandelbrot set is $M = \{ c \in \mathbb{C} : J_c \text{ is connected} \}$. Call the closed disc of radius $2$ centered at the origin $D = \{ c \in \mathbb{C} : |c| \le 2 \}$, now $M \subseteq D$.
Question: does $c \in M$ imply $J_c \subseteq D$ ?