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Homework on 4 November 2019:

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


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Created: 4 Nov 2019
Last modified: 4 Nov 2019 at 2:15 PM
Comments to: dpvc@union.edu
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