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- Let $f\colon X\to Y$ be a function.
- Prove that $f(A\cap B)\subseteq f(A)\cap f(B)$ for all subsets $A$ and $B$ of $X$.
- Give an example of a function $f$ and sets $A$ and $B$ that shows that the subset need not be an equality.
- What condition on $f$ would guarantee equality? (Prove that you are right).
- Let $f\colon X\to Y$ be a function.
- Show that $f(A)-f(B)\subseteq f(A-B)$ for all subsets $A$ and $B$ of $X$.
- Give an example of a function $f$ and sets $A$ and $B$ that shows that the subset need not be an equality.
- What condition on $f$ would guarantee equality? (Prove that you are right).
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