Hello, I would be grateful if I could receive some assistance with the following question:

Let $\displaystyle \mathcal{C}$ be a $\displaystyle \sigma-field$, and let $\displaystyle A \in \mathcal{C}$.

Define $\displaystyle \mathcal{C}_{\mathcal{A}}=\{C:C=A \cap B \text{ for some } B \in\mathcal{C}\}$

Show that $\displaystyle \mathcal{C}_{\mathcal{A}}$ is a $\displaystyle \sigma-field$. [Note: Complements of sets are formed with respect to $\displaystyle A$]

Thank you so much in advance to anybody who helps me with this. This material is so confusing for me, and I'm sure I can get it, but it will take time, practice, and guidance.