1. | a. |
Reagan’s vice president was the 41st president. Reagan’s vice president = the 41st president [λx (x’s vice president)] Reagan = [λx (the xth president)] 41
vr = pf
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b. |
Tom found a fly in his soup and he called the waiter Tom found a fly in his soup ∧ Tom called the waiter Tom found a fly in Tom’s soup ∧ Tom called the waiter [λxy (x found a fly in y)] Tom Tom’s soup ∧ [λxy (x called y)] Tom the waiter Ft(Tom’s soup) ∧ Ctr Ft([λx (x’s soup)] Tom) ∧ Ctr
Ft(st) ∧ Ctr
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c. |
Tom found the book everyone had talked to him about and he bought a copy of it Tom found the book everyone had talked to him about ∧ Tom bought a copy of the book everyone had talked to him about Tom found the book everyone had talked to Tom about ∧ Tom bought a copy of the book everyone had talked to Tom about [λxy (x found y)] Tom the book everyone had talked to Tom about ∧ [λxy (x bought a copy of y)] Tom the book everyone had talked to Tom about Ft(the book everyone had talked to Tom about) ∧ Bt(the book everyone had talked to Tom about) Ft([λx (the book everyone had talked to x about)] Tom) ∧ Bt([λx (the book everyone had talked to x about)] Tom)
Ft(bt) ∧ Bt(bt)
[B: λxy (x bought a copy of y); F: λxy (x found y); b: λx (the book everyone had talked to x about); t: Tom] |
d. |
Wabash College is located in Crawfordsville, which is the seat of Montgomery County Wabash College is located in Crawfordsville ∧ Crawfordsville is the seat of Montgomery County [λxy (x is located in y)] Wabash College Crawfordsville ∧ Crawfordsville = the seat of Montgomery County Lbc ∧ c = [λx (the seat of x)] Montgomery County
Lbc ∧ c = sm
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e. |
Sue and Tom set the date of their wedding but didn’t decide on its location
Sue and Tom set the date of their wedding
Sue and Tom set the date of Sue and Tom’s wedding
[λxyz (x and y set z)] Sue Tom the date of Sue and Tom’s wedding
Sst(the date of Sue and Tom’s wedding)
Sst([λx (the date of x)] Sue and Tom’s wedding)
Sst(d(Sue and Tom’s wedding)) ∧ ¬ Dst(l(Sue and Tom’s wedding))
Sst(d([λxy (x and y’s wedding)] Sue Tom))
Sst(d(wst)) ∧ ¬ Dst(l(wst))
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2. | a. |
([λxy (x has spoken to y)] Ann Bill ∧ ¬ [λxy (x has spoken to y)] Ann ([λx (x’s father)] Carol)) → ¬ Bill = [λx (x’s father)] Carol (Ann has spoken to Bill ∧ ¬ [λxy (x has spoken to y)] Ann Carol’s father) → ¬ Bill = Carol’s father (Ann has spoken to Bill ∧ ¬ Ann has spoken to Carol’s father) → ¬ Bill is Carol’s father (Ann has spoken to Bill ∧ Ann hasn’t spoken to Carol’s father) → Bill isn’t Carol’s father Ann has spoken to Bill but not to Carol’s father → Bill isn’t Carol’s father If Ann has spoken to Bill but not to Carol’s father, then Bill isn’t Carol’s father |
b. |
(B([λx (x’s father)] Ann)([λx (x’s mother)] Bill) ∨ S([λx (x’s mother)] Ann)([λx (x’s father)] Bill)) → [λxy (x and y are cross-cousins)] Ann Bill ([λxy (x is a brother of y)] Ann’s father Bill’s mother ∨ [λxy (x is a sister of y)] Ann’s mother Bill’s father) → Ann and Bill are cross-cousins (Ann’s father is a brother of Bill’s mother ∨ Ann’s mother is a sister of Bill’s father) → Ann and Bill are cross-cousins Ann’s father is a brother of Bill’s mother or Ann’s mother is a sister of Bill’s father → Ann and Bill are cross-cousins If Ann’s father is a brother of Bill’s mother or Ann’s mother is a sister of Bill’s father, then Ann and Bill are cross-cousins |
c. |
Pab(m([λx (x’s proposal)] Bill)([λx (x’s proposal)] Carol))
Pab([λxy (the best compromise between x and y)] Bill’s proposal Carol’s proposal)
[λxyz (x persuaded y to accept z)] Ann Bill the best compromise between Bill’s proposal and Carol’s proposal
Ann persuaded Bill to accept the best compromise between his and Carol’s proposals
Ann persuaded each of Bill and Carol to accept the best compromise between their proposals |