🚧 Setup for 4.8

chapter_4/test_yourself.md

@@ -223,3 +223,23 @@ $\forall x \in D, \text{ if } \neg Q(x) \text{ then } \neg P(x)$
    you suppose that ______ and you show that ______.
 
 $Q(x)$ is false; $P(x)$ is false.
+
+---
+
+**Test Yourself**
+
+Page 256
+
+1. The ancient Greeks discovered that in a right triangle where both legs have
+   length $1$, the ratio of the length of the hypotenuse to the length of one of
+   the legs is not equal to a ratio of ______.
+
+2. One way to prove that $\sqrt{2}$ is an irrational number is to assume that
+   $\sqrt{2} = \dfrac{m}{n}$ for some integers $m$ and $n$ that have no common
+   factor greater than $1$, use the lemma that says that if the square of an
+   integer is even then ______, and eventually show that $m$ and $n$ ______.
+
+3. One way to prove that there are infinitely many prime numbers is to assume
+   that there is a largest prime number $p$, construct the number ______, and
+   then show that this number has to be divisible by a prime number that is
+   greater than ______.