110 lines
2.2 KiB
Text
110 lines
2.2 KiB
Text
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#import "./dvd.typ": *
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#show: dvdtyp.with(
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title: "Pset 1",
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author: "Youwen Wu",
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)
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#set heading(
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numbering: (
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num => {
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return "1." + str(num)
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}
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),
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)
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Problems:
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1.1: \#1ceij, 2c, 3cdeghjL, 4cdefh, 6, 7cg, 10ce, 11bei, 12a, 13
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1.2: \#1bd, 2bd, 3, 5cfgh, 6bcg, 7be, 10bfg, 12bc, 13, 16cde
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= Exercises
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1. \
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c. #[
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$x/2$ is a rational number.
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True.
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] \
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e. #[
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Either $pi$ is rational and $17$ is a prime, or $7 < 13$ and $81$ is a perfect square.
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True.
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] \
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i. #[
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It is not the case that $39$ is prime, or that 64 is a power of 2.
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False.
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] \
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j. #[
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There are more than three false statements in this book, and this statement is one of them.
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False.
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]
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2c. #[
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$P$ is $5^2 + 12^2 = 13^2$ and $Q$ is $sqrt(2) + sqrt(3) = sqrt(2 + 3)$
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$P and Q: "false"$
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$P or Q: "true"$
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]
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3. #[
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\
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c. $P and not Q$
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#[
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#table(
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columns: 3,
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align: center,
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[$P$], [$Q$], [$P and not Q$],
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[T], [T], [F],
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[T], [F], [T],
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[F], [T], [F],
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[F], [F], [F],
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)
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] \
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d. $P and (Q or not Q)$
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#[
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#table(
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columns: 5,
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align: center,
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[$P$], [$Q$], [$not Q$], [$Q or not Q$], [$P and (Q or not Q)$],
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[T], [T], [F], [T], [T],
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[T], [F], [T], [T], [T],
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[F], [T], [F], [T], [F],
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[F], [F], [T], [T], [F],
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)
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] \
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e. $(P and Q) or not Q$ \
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#[
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#table(
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columns: 5,
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align: center,
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[$P$], [$Q$], [$P and Q$], [$not Q$], [$(P and Q) or not Q$],
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[T], [T], [T], [F], [T],
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[F], [T], [F], [F], [F],
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[T], [F], [F], [T], [T],
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[F], [F], [F], [T], [T],
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)
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] \
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g. $(P or S) and (P or K)$
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#table(
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columns: (1fr, 1fr, 1fr, 1fr, 1fr, 2fr),
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align: center,
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[$P$], [$S$], [$K$], [$P or S$], [$P or K$], [$(P or S) and (P or K)$],
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[T], [T], [T], [T], [T], [T],
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[T], [T], [F], [T], [T], [T],
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[T], [F], [T], [T], [T], [T],
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[T], [F], [F], [T], [T], [T],
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[F], [T], [T], [T], [T], [T],
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[F], [T], [F], [T], [F], [F],
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[F], [F], [T], [F], [T], [T],
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[F], [F], [F], [F], [F], [F],
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)
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]
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= Exercises
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