🚧 Fin 4.1

chapter_4/test_yourself.md

@@ -4,16 +4,31 @@ Page 194
 
 1. An integer is even if, and only if, ______.
 
+it equals twice some integer.
+
 2. An integer is odd if, and only if, ______.
 
+it equals twice some integer plus 1.
+
 3. An integer $n$ is prime if, and only if, ______.
 
+$n$ is greater than $1$ and if $n$ equals the product of any two positive
+integers, then one of the integers equals $1$ and the other equals $n$.
+
 4. The most common way to disprove a universal statement is to find ______.
 
+a counterexample.
+
 5. According to the method of generalizing from the generic particular, to show
    that every element of a set satisfies a certain property, suppose $x$ is a
    ______, and show that ______.
 
+particular but arbitrarily chosen element of the set; $x$ satisfies the given
+property.
+
 6. To use the method of direct proof to prove a statement of the form, "For
    every $x$ in a set $D$, if $P(x)$ then $Q(x)$," one supposes that ______ and
    one shows that ______.
+
+$x$ is a particular but arbitrarily chosen element of the set $D$ that makes the
+hypothesis $P(x)$ true; $x$ makes the conclusion $Q(x)$ true.