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Let $\text{S}$ and $\text{T}$ be two non-empty sets and $f : \text{S} \rightarrow \text{T}$ be a function such that $f (\text{A} \cap \text{B}) = f (\text{A}) \cap f(\text{B})$ for all subsets $\text{A}$ and $\text{B}$ of $\text{S}$. Then

  1. there exist $\text{A} \subset \text{S}$ such that $f^{-1} f(\text{A}) \neq \text{A}$

  2. $f$ is one- to- one

  3. there exist disjoint subsets $\text{A}, \text{B}$ of $\text{S}$ such that $f(\text{A}) \cap f(\text{B}) \neq \phi $

  4. none of the above statements is necessarily true.

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