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**noob mathematician** This is how the question reads:

Let $\displaystyle f$ be a function mapping $\displaystyle \Omega$ to another space $\displaystyle E$ with a $\displaystyle \sigma$-algebra $\displaystyle \mathcal{E}$. Let $\displaystyle \mathcal{A}=(A\subset \Omega: \text{there exists B} \in E \text{ with A}=f^{-1}(B))$. Show that $\displaystyle \mathcal{A}$ is a $\displaystyle \sigma$-algebra on $\displaystyle \Omega$.

How do I go about mapping the function? Sorry, I am not very sure with the concept of probability space