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
v of r is p of f

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
both F fits t ’n s of t and C fits t ’n r

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)
both F fits t ’n b of t and B fits t ’n b of t

[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]

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
both L fits b ’n c and c is s of m

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 didn’t decide on the location of their wedding

Sue and Tom set the date of Sue and Tom’s wedding
∧ ¬ Sue and Tom decided on the location of Sue and Tom’s wedding

[λxyz (x and y set z)] Sue Tom the date of Sue and Tom’s wedding
∧ ¬ [λxyz (x and y decided on z)] Sue Tom the location of Sue and Tom’s wedding

Sst(the date of Sue and Tom’s wedding)
∧ ¬ Dst(the location of Sue and Tom’s wedding)

Sst([λx (the date of x)] Sue and Tom’s wedding)
∧ ¬ Dst([λx (the location 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))
∧ ¬ Dst(l([λxy (x and y’s wedding)] Sue Tom))

Sst(d(wst)) ∧ ¬ Dst(l(wst))
both S fits s, t, ’n d of (w of s ’n t) and not D fits s, t, ’n l of (w of s ’n t)

([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([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

Pab(m([λx (x’s proposal)] Bill)([λx (x’s proposal)] Carol))
∧ Pac(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)
∧ Pac([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
∧ [λxyz (x persuaded y to accept z)] Ann Carol 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 Carol to accept the best compromise between Bill’s proposal and hers

Ann persuaded each of Bill and Carol to accept the best compromise between their proposals