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