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✏️ Fixed wording and answers

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tomit4 2026-05-12 15:31:01 -07:00
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chapter_1/1_1/practice_problems.md
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@ -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.

23
chapter_1/1_1/preview_activity.md
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@ -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.