diff --git a/chapter_1/1_1/practice_problems.md b/chapter_1/1_1/practice_problems.md
index 6e5a24b..1d87050 100644
--- a/chapter_1/1_1/practice_problems.md
+++ b/chapter_1/1_1/practice_problems.md
@@ -25,7 +25,7 @@ $$ \exists x \left(P(x) \wedge Q(x)\right) $$
 If we say that $x$ is "it", and $P(x)$ is "the way it ought to be", and $Q(x)$
 is "Mom is coming round to put it back," then we can write this as:
 
-$$ P(x) \to Q(x) $$
+$$ \exists x \left(P(x) \to Q(x)\right) $$
 
 This is an atomic statement, as both $P(x)$ and $Q(x)$ cannot be divided into
 smaller elements.
diff --git a/chapter_1/1_1/preview_activity.md b/chapter_1/1_1/preview_activity.md
index b8a7326..678b5ba 100644
--- a/chapter_1/1_1/preview_activity.md
+++ b/chapter_1/1_1/preview_activity.md
@@ -1,3 +1,7 @@
+Before reading on to the main content of the section, complete this preview
+activity to start thinking about the types of questions this section will
+address.
+
 1.
 
 Q: Which of the following sentences should count as statements? That is, for
@@ -35,10 +39,12 @@ reasonable responses to this claim, from a logical point of view?
 
     D. The statement is false because everyone who likes pineapple on pizza does NOT like pineapple in smoothies.
 
-A: From a logical point of view, statements A, C, and D are all reasonable
-responses. Only B is not reasonable because it is a conclusion based on an
-assertion that was never made (i.e. the roommate never claimed that pizza
-smoothie is good).
+A: From a logical point of view, statements A an C are both reasonable
+responses. B is not reasonable because it is a conclusion based on an assertion
+that was never made (i.e. the roommate never claimed that pizza smoothie is
+good). D is not logically valid because it concludes by making a further
+assertion that everyone who likes pineapple on pizza does NOT like pineapple in
+smoothies, which the original assertion does not include.
 
 3.
 
@@ -88,8 +94,7 @@ knight. What can you say to this?
 
 A:
 
-C is the only verifiable logical argument. Since we only have each troll's word
-on whether they are a knave(lying) or a knight (telling the truth), there is
-always the potential that they are lying. Without another external way of
-validating whether they are a knave or a knight, we cannot validate the
-roommate's assertion.
+A is correct. If it is not true that all trolls are knaves, then there must be
+at least 1 knight, since those are the only two states a Troll can be in
+(truthful=knight, lying=knave), and if they _all_ are NOT knaves, then at least
+one of them _must_ be a knight.