Are supersets of measurable sets measurable?

Question

Challenging conventional wisdom question

Let $(S, \Sigma, \mu) = (\mathbb{R}, \mathscr{M}(\mathbb{R}), \lambda)$, where $\mathscr{M}(\mathbb{R})$ is the collection of all $\lambda$-measurable subsets of $\mathbb{R}$

If $A \in \Sigma$ and $B \subseteq A$, it does not follow that $B \in \Sigma$.

However, if $C \supseteq A$, do we have $C \in \Sigma$?

I guess we can have $C = A \cup V$ where $V \notin \Sigma$ (eg Vitali set) and $V \subsetneq A$, right?

Answer 1

Recall that every set is a superset of the empty set.