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Homework 1

3 min read

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Module 1

    • a) {−1,1}
    • b) {1,2,3,4,5,6,7,8,9,10,11}
    • c) {4,9,16,25,36,49,64,81}
    • d) ⌀
    • Nonstop airlines is a subset of airline flights
    • Neither are a subset
    • Flying squirrels is a subset of flying creatures
    • False
    • False
    • False
    • True
    • False
    • False
    • True
    • 1
    • 1
    • 2
    • 3
    • a) {⌀,{𝑎}}
    • b) {⌀,{𝑎},{𝑏},{𝑏,𝑎}}
    • c) {⌀,{⌀},{{⌀}},{⌀,{⌀}}}
    • a) |𝑃(𝑆)|=2|𝑆|→23→8
    • b) |𝑃(𝑆)|=24→16
    • c) |𝑃(𝑆)|=21→2
    • a) {(𝑎,𝑦),(𝑎,𝑧),(𝑏,𝑦),(𝑏,𝑧),(𝑐,𝑦),(𝑐,𝑧),(𝑑,𝑦),(𝑑,𝑧)}
    • a) {(𝑦,𝑎),(𝑧,𝑎),(𝑦,𝑏),(𝑧,𝑏),(𝑦,𝑐),(𝑧,𝑐),(𝑦,𝑑),(𝑧,𝑑)}

Module 2

    • Students who live within one mile that walk to class
    • Students who live within one mile or walk to class
    • Students who live within one mile that do not walk to class
    • Students who walk to class that do not live within one mile
    • a) {0,1,2,3,4,5,6}
    • b) {3,6}
    • c) {1,2,4,5}
    • d) {0,6}
    • 𝐴={1,5,7,8,3,6,9}
    • 𝐵={2,10,3,6,9}
  • 21b.
    • (𝐴∩𝐵)∪(𝐴∩𝐵)→𝐴∩(𝐵∪𝐵)→𝐴∩𝑈=𝐴
    • a) {4,6}
    • b) {0,1,2,3,4,5,6,7,8,9,10}
    • c) {4,5,6,8,10}
    • d) {0,2,4,5,6,7,8,9,10}
    • 𝐴∩(𝐵−𝐶)
    • (𝐴∩𝐵)∪(𝐴∩𝐶)
    • (𝐴∩𝐵)∪(𝐴∩𝐶)

Module 3

    • a)
      • 𝑎0=20+1→1+1→2
      • 𝑎1=21+1→2+1→3
      • 𝑎2=22+1→4+1→5
      • 𝑎3=23+1→8+1→9
    • b)
      • 𝑎0=(0+1)0+1→11→1
      • 𝑎1=(1+1)1+1→22→4
      • 𝑎2=(2+1)2+1→33→9
      • 𝑎3=…→44→16
      • 𝑎4=…→25
    • c)
      • 𝑎0=⌊02⌋→0
      • 𝑎1=⌊12⌋→0
      • 𝑎2=⌊22⌋→1
      • 𝑎3=⌊32⌋→1
      • 𝑎4=⌊42⌋→2
    • d) (assuming | is bitwise OR)
      • 𝑎0=⌊0|2⌋+⌈02⌉→⌊2⌋+0→2
      • 𝑎1=⌊1|2⌋+⌈12⌉→⌊3⌋+1→4
      • 𝑎2=⌊2|2⌋+⌈22⌉→⌊2⌋+1→3
      • 𝑎3=⌊3|2⌋+⌈32⌉→⌊3⌋+2→5
      • 𝑎4=⌊4|2⌋+⌈42⌉→|6|+2→8
    • a)
      • 𝑎1=6×2−1→11
      • 𝑎2=6×11−1→65
      • 𝑎3=6×65−1→389
      • 𝑎4=6×389−1→2333
      • 𝑎5=6×2333−1→13997
    • b)
      • 𝑎1=2
      • 𝑎2=22→4
      • 𝑎3=42→16
      • 𝑎4=162→256
      • 𝑎5=2562→65536
    • c)
      • 𝑎1=2
      • 𝑎2=2+3×1→2+3→5
      • 𝑎3=5+3×2→5+6→11
      • 𝑎3=11+3×5→11+15→26
      • 𝑎4=26+3×11→59
      • 𝑎5=59+3×26→137
    • d)
      • 𝑎0=1
      • 𝑎1=1
      • 𝑎2=2×1+22×1→6
      • 𝑎3=3×6+32×1→27
      • 𝑎4=4×27+42×6→16777324
    • e)
      • 𝑎2=0
      • 𝑎3=2+1→3
      • 𝑎4=3+2→5
      • 𝑎5=4+0→4
      • 𝑎6=5+3→8
    • a) (1+1)+(2+1)+(3+1)+(4+1)+(5+1)=20
    • b) (−2)0+(−2)1+(−2)2+(−2)3+(−2)4=11
    • c) 30
    • d) (21−20)+(22−21)+(23−22)+…+(29−20)=511

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