2.1.xa. Exercise answers

1. a.

Mike visited LondonMike visited Paris

L ∧ P
both L and P

L: Mike visited London; P: Mike visited Paris

  b.

Ann wanted white wineBill and Carol wanted red wine

Ann wanted white wine ∧ (Bill wanted red wineCarol wanted red wine)

A ∧ (B ∧ C)
both A and both B and C

A: Ann wanted white wine; B: Bill wanted red wine; C: Carol wanted red wine

  c.

It will rain and clear offit will rain

(it will rainit will clear off) ∧ it will rain

(R ∧ C) ∧ R
both both R and C and R

C: it will clear off; R: it will rain

  d.

That is a marketthat is new relative to other markets but growing

That is a market(that is new relative to other marketsthat is growing)

M ∧ (N ∧ G)
both M and both N and G

G: that is growing; M: that is a market; N: that is new relative to other markets

  e.

Confucius is affable but dignifiedConfucius is austere but not harshConfucius is polite but completely at ease

(Confucius is affableConfucius is dignified) ∧ (Confucius is austereConfucius is not harsh) ∧ (Confucius is politeConfucius is completely at ease)

(A ∧ D) ∧ (S ∧ H) ∧ (P ∧ E)
(both A and D) and (both S and H) and (both P and E)

A: Confucius is affable; D: Confucius is dignified; E: Confucius is completely at ease; H: Confucius is not harsh; P: Confucius is polite; S: Confucius is austere

  f.

Tim lost his glasses and his walletTim’s glasses and wallet were each returned

(Tim lost his glassesTim lost his wallet) ∧ (Tim’s glasses were returnedTim’s wallet was returned)

(G ∧ W) ∧ (R ∧ T)
both both G and W and both R and T

G: Tim lost his glasses; R: Tim’s glasses were returned; T: Tim’s wallet was returned; W: Tim lost his wallet

  g.

Tim lost his glasses and his walletone person found both Tim’s glasses and his wallet

(Tim lost his glassesTim lost his wallet) ∧ one person found both Tim’s glasses and his wallet

(G ∧ W) ∧ O
both both G and W and O

G: Tim lost his glasses; O: one person found both Tim’s glasses and his wallet; W: Tim lost his wallet

NoteOne person found both Tim’s glasses and his wallet cannot be analyzed further because One person found Tim’s glasses ∧ one person found Tim’s wallet does not imply that the same person found both.

2. a. A ∧ (B ∧ C)
  b. (A ∧ B) ∧ C
  c. both both A and B and both C and D
  d. both A and both both B and C and D
  e. both both A and both B and C and D
  f. ((A ∧ B) ∧ C) ∧ D
3. a.

(Fred visited VeniceFred visited Florence) ∧ Fred spent a week in Rome

Fred visited Venice and FlorenceFred spent a week in Rome

Fred visited Venice and Florence, and he spent a week in Rome

  b.

(he was a judge ∧ (he was sternhe was fair)) ∧ he had an excellent knowledge of the law

(he was a judgehe was stern but fair) ∧ he had an excellent knowledge of the law

He was a stern but fair judge who had an excellent knowledge of the law

  c.

(we arrived coldwe arrived tiredwe arrived hungry) ∧ (we left warmwe left stuffedwe left sleepy)

We arrived cold, tired, and hungrywe left warm, stuffed, and sleepy

We arrived cold, tired, and hungry; and we left warm, stuffed, and sleepy

  d.

Old King Cole was a merry old soulOld King Cole was a merry old soul

Old King Cole was a merry old soul, and a merry old soul was he

4. Numbers below the tables indicate the order in which values were computed
  a.
ABCA(BC)
TTFF
21
  b.
ABCD((AD)C)(BA)
TTFTTFT
1231
Glen Helman 01 Aug 2011