Math 199 (Assignments)

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1. On the quiz today, you showed, for all sets $A$, $B$, and $X$, that $X-(A\cap B) \subseteq (X-A)\cup(X-B)$. Show that this is actually an equality, not just a subset.
2. In class, we showed that, for any sets $A$, $B$, and $C$, $A\cup(B\cap C) \subseteq (A\cup B)\cap (A\cup C)$. Show that this is actually an equality. (I.e., do the second half of the proof, which we didn't finish.)
3. Show that $\sqrt{3}$ is irrational.

   Hint: This will work very similarly to the proof we did in class for $\sqrt 2$. But you will need to prove the analog of our theorem about $2\mid m^2$ implying $2\mid m$ that we used twice in the proof for $\sqrt{2}$.

Math 199 (Fall 2019) web pages Created: 16 Oct 2019 Last modified: 16 Oct 2019 at 5:27 PM Comments to: dpvc@union.edu

Assignments