#import "./dvd.typ": *

#show: dvdtyp.with(
  title: "Pset 1",
  author: "Youwen Wu",
)

#set heading(
  numbering: (
    num => {
      return "1." + str(num)
    }
  ),
)

Problems:

1.1: \#1ceij, 2c, 3cdeghjL, 4cdefh, 6, 7cg, 10ce, 11bei, 12a, 13

1.2: \#1bd, 2bd, 3, 5cfgh, 6bcg, 7be, 10bfg, 12bc, 13, 16cde

= Exercises

1. \
  c. #[
  $x/2$ is a rational number.

  True.
  ] \
  e. #[
  Either $pi$ is rational and $17$ is a prime, or $7 < 13$ and $81$ is a perfect square.

  True.
  ] \
  i. #[
    It is not the case that $39$ is prime, or that 64 is a power of 2.

    False.
  ] \
  j. #[
  There are more than three false statements in this book, and this statement is one of them.

  False.
  ]

2c. #[
  $P$ is $5^2 + 12^2 = 13^2$ and $Q$ is $sqrt(2) + sqrt(3) = sqrt(2 + 3)$

  $P and Q: "false"$

  $P or Q: "true"$
]

3. #[
    \
    c. $P and not Q$
    #[
      #table(
        columns: 3,
        align: center,
        [$P$], [$Q$], [$P and not Q$],
        [T], [T], [F],
        [T], [F], [T],
        [F], [T], [F],
        [F], [F], [F],
      )
    ] \
    d. $P and (Q or not Q)$
    #[
      #table(
        columns: 5,
        align: center,
        [$P$], [$Q$], [$not Q$], [$Q or not Q$], [$P and (Q or not Q)$],
        [T], [T], [F], [T], [T],
        [T], [F], [T], [T], [T],
        [F], [T], [F], [T], [F],
        [F], [F], [T], [T], [F],
      )
    ] \
    e. $(P and Q) or not Q$ \
    #[
      #table(
        columns: 5,
        align: center,
        [$P$], [$Q$], [$P and Q$], [$not Q$], [$(P and Q) or not Q$],
        [T], [T], [T], [F], [T],
        [F], [T], [F], [F], [F],
        [T], [F], [F], [T], [T],
        [F], [F], [F], [T], [T],
      )
    ] \
    g. $(P or S) and (P or K)$
    #table(
      columns: (1fr, 1fr, 1fr, 1fr, 1fr, 2fr),
      align: center,
      [$P$], [$S$], [$K$], [$P or S$], [$P or K$], [$(P or S) and (P or K)$],
      [T], [T], [T], [T], [T], [T],
      [T], [T], [F], [T], [T], [T],
      [T], [F], [T], [T], [T], [T],
      [T], [F], [F], [T], [T], [T],
      [F], [T], [T], [T], [T], [T],
      [F], [T], [F], [T], [F], [F],
      [F], [F], [T], [F], [T], [T],
      [F], [F], [F], [F], [F], [F],
    )
  ]


= Exercises