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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 $Q(x)$ 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: 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 This is an atomic statement, as both $P(x)$ and $Q(x)$ cannot be divided into
smaller elements. 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. 1.
Q: Which of the following sentences should count as statements? That is, for 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. 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 A: From a logical point of view, statements A an C are both reasonable
responses. Only B is not reasonable because it is a conclusion based on an responses. B is not reasonable because it is a conclusion based on an assertion
assertion that was never made (i.e. the roommate never claimed that pizza that was never made (i.e. the roommate never claimed that pizza smoothie is
smoothie is good). 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. 3.
@ -88,8 +94,7 @@ knight. What can you say to this?
A: A:
C is the only verifiable logical argument. Since we only have each troll's word A is correct. If it is not true that all trolls are knaves, then there must be
on whether they are a knave(lying) or a knight (telling the truth), there is at least 1 knight, since those are the only two states a Troll can be in
always the potential that they are lying. Without another external way of (truthful=knight, lying=knave), and if they _all_ are NOT knaves, then at least
validating whether they are a knave or a knight, we cannot validate the one of them _must_ be a knight.
roommate's assertion.