38 lines
777 B
Text
38 lines
777 B
Text
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#import "@youwen/zen:0.1.0": *
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#import "@preview/ctheorems:1.1.3": *
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#show: zen.with(
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title: "Homework 1",
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author: "Youwen Wu",
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date: "Winter 2025",
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)
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1. #[
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#set enum(numbering: "a)", spacing: 2em)
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+ #[
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We know that $B$ and $B'$ are disjoint. That is, $B sect B' =
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emptyset$. Additionally,
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$
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E = (A sect B) subset B \
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F = (A sect B') subset B' \
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$
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Then we note
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$
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forall x in E, x in B, x in.not B' \
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forall y in F, y in B, y in.not B'
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$
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So clearly $E$ and $F$ have no common elements, and
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$
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E sect F = emptyset
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$
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]
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+ #[
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$
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E union F &= (A sect B) union (A sect B') \
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&=
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$
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]
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]
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