style: format with typstfmt
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@ -49,15 +49,16 @@ Section 001
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radius: 4pt,
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stroke: luma(50%) + .5pt,
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fill: luma(90%),
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)[If you are interested in viewing the source code of this document, you can do so by clicking
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)[If you are interested in viewing the source code of this document, you can do so
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by clicking
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#text(
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blue,
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link(
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"https://gitlab.orion-technologies.io/philler/college/-/blob/Development/Spring-2023/CS-2233/Assignment-1/Solution.typ?ref_type=heads",
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"here",
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),
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). This document was written in Typst and a bit of infinite _withering_ pain in Neovim, a Vim
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derivative. Here's to hoping everything below is correct.],
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). This document was written in Typst and a bit of infinite _withering_ pain in
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Neovim, a Vim derivative. Here's to hoping everything below is correct.],
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)
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= Problems
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@ -125,17 +126,17 @@ Section 001
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Expressing "You understand propositional logic if you passed CS 2233" logically
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would be:
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#m[s → q]
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#m[s → p]
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Now slightly rewriting the statement with our logic embedded, "If you can
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register for CS 3343, then you have passed CS 2233 and $(s → q)$".
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register for CS 3343, then you have passed CS 2233 and $(s → p)$".
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Then further refining the statement: "If you can register for CS 3343 then $p ∧ (s → q)$.
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Then further refining the statement: "If you can register for CS 3343 then $p ∧ (s → p)$.
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And with a final refinement: $r → p ∧ (s → q)$
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And with a final refinement: $r → p ∧ (s → p)$
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Thus the final expression logically would be:
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][$r → p ∧ (s → p)$]
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][$r → (p ∧ (s → p))$]
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]
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#problem(
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3,
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@ -379,8 +380,8 @@ Section 001
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d. [10 points] By creating a sequence of logical equivalences and annotating
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each step
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#solve[Notice by step three, both logical sequences are equivalent.][
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#table(columns: 2, [
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*$¬q → (p ∧ r)$*
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#table(columns: 2, align: left, [
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#align(center)[*$¬q → (p ∧ r)$*]
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#grid(columns: 2, row-gutter: .5em, column-gutter: 1em)[
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1. $¬¬q ∨ (p ∧ r)$
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][Conditional Identities][
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@ -388,8 +389,7 @@ Section 001
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][Double Negation Law][
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3. $(q ∨ p) ∧ (q ∨ r)$
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][Distributive Laws]
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], [
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#align(left)[*$(¬q → r) ∧ (q ∨ p)$*]
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], [#align(center)[*$(¬q → r) ∧ (q ∨ p)$*]
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#grid(columns: 2, row-gutter: .5em, column-gutter: 1em)[
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1. $(¬¬q ∨ r) ∧ (q ∨ p)$
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][Conditional Identities][
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