Why is the following answer to a question on topology true?

Question

Let X be a topological space. Let A,B ⊂ X and A ⊂ B.

Why is $ \bar{A} \subset \bar{B}$ true?

Answer 1

$\bar{A}$ is the smallest closed set containing $A$. Now $\bar{B}$ is closed by definition and contains $B$, hence $A$, and the statement follows.