93 lines
3.5 KiB
Plaintext
93 lines
3.5 KiB
Plaintext
01. TFTF----FF
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02. a) Linda is older than Sanjay (given that age is continuous)
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b) Mei does not make more money than Isabella (salaries are discrete)
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c) Moshe is shorter than Monica (height is continuous)
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d) Abby is not richer than Ricardo (is wealth continuous?)
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e) Quincy is not smarter than Venkat (unquantifiable ∴ continuous)
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f) 2 + 1 /= 3
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g) The summer in Maine is not hot and sunny
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i) Jennifer and Teja are not friends
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03. TTFF
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4 a) I did not buy a lottery ticket this week
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b) I bought a lottery ticket this week and I won the million dollar jackpot
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c) If I bought a lottery ticket this week, I won the million dollar jackpot
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d) I bought a lottery ticket this week, or I won the million dollar jackpot
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e) I bought a lottery ticket if and only if I won the million dollar jackpot
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f) If I didn't buy a lottery ticket this week, I didn't win the million dollar jackpot
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g) I didn't buy a lottery ticket this week, and I didn't win the million dollar jackpot
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h) I didn't buy a lottery ticket this week, or I did buy a lottery ticket this week and I won the million dollar jackpot
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-> If I bought a lottery ticket this week, I won the million dollar jackpot
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05. a) !p
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b) p & !q
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c) p -> q
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d) !p -> !q
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e) p -> q
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f) q & !p
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g) p <-> q
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06. a) r & !p
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b) !p & q & r
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c) r -> (!p <-> q)
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d) !q & !p & r
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e) q -> (!r & !p)
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f) (p & r) -> !q
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07. TFTF
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08. FTTT
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09. a) If one does not wash the boss's car, one is not promoted
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b) If there exist winds from the south, there will exist a spring thaw
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c) If the computer was bought less than a year ago, the warranty is good
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d) If Willy cheats, he is caught
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e) If you do not pay a subscription fee, you cannot access the website
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f) If one knows the right people, one is elected
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g) If Carol is on a boat, she gets seasick
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10. a) p !p p -> !p
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T F F
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F T T
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b) p !p p <-> !p
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T F F
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F T F
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c) p q p ^ (p | q) (== !p & q)
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T T F
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T F F
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F T T
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F F F
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d) p q (p | q) -> (p & q)
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T T T
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T F F
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F T T
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F F T
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11. OR AND XOR
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111_1111 000_0000 111_1111
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1111_1010 1010_0000 0101_1010
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10_0111_1001 00_0100_0000 10_0011_1001
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12. a) 11000
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b) 10001
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13.
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a) p q r (p | q) ((p | q) | r) (q | r) (p | (q | r))
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T T T T T T T
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T T F T T T T
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T F T T T T T
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T F F T T F T
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F T T T T T T
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F T F T T T T
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F F T F T T T
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F F F F F F F
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b) p q r (p & q) ((p & q) & r) (q & r) (p & (q & r))
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T T T T T T T
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T T F T F F F
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T F T F F F F
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T F F F F F F
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F T T F F T F
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F T F F F F F
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F F T F F F F
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F F F F F F F
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14. a) Jan is not rich or is not happy
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b) Carlos will not run and will not bicycle tomorrow
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c) Mei does not walk and does not take the bus to class
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d) Ibrahim is not smart or is not hard-working
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15. (p -> q) & (p -> r)
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≣ (!p | q) & (!p | r) # Definition of ->
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≣ (!p | (q & r)) # Distribution of | over &
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≣ p -> (q & r) # Definition of -> |