Ann introduced Bill to Carol

[ _ introduced _ to _ ] Ann Bill Carol

Iabc
I fits a, b, ən c

I: [ _ introduced _ to _ ]; a: Ann; b: Bill; c: Carol

Ann gave the book to either Bill or Carol

Ann gave the book to Bill ∨ Ann gave the book to Carol

[ _ gave _ to _ ] Ann the book Bill ∨ [ _ gave _ to _ ] Ann the book Carol

Gakb ∨ Gakc
either G fits a, k, ən b or G fits a, k, ən c

G: [ _ gave _ to _ ]; a: Ann; b: Bill; c: Carol; k: the book

Ann gave the book to Bill and he gave it to Carol

Ann gave the book to Bill ∧ Bill gave the book to Carol

[ _ gave _ to _ ] Ann the book Bill ∧ [ _ gave _ to _ ] Bill the book Carol

Gakb ∧ Gbkc
both G fits a, k, ən b and G fits b, k, ən c

G: [ _ gave _ to _ ]; a: Ann; b: Bill; c: Carol; k: the book

Tom had the package sent to Sue, but it was returned to him

Tom had the package sent to Sue ∧ the package was returned to Tom

[ _ had _ sent to _ ] Tom the package Sue ∧ [ _ was returned to _ ] the package Tom

Htps ∧ Rpt
both H fits t, p, ən s and R fits p ən t

H: [ _ had _ sent to _ ]; R: [ _ was returned to _ ]; p: the package; s: Sue; t: Tom

Georgia will see Ed if she gets to Denver before Saturday

Georgia will see Ed ← Georgia will get to Denver before Saturday

[ _ will see _ ] Georgia Ed ← [ _ will get to _ before _ ] Georgia Denver Saturday

Sge ← Ggds
Ggds → Sge
if G fits g, d, ən s then S fits g ən e

G: [ _ will get to _ before _ ]; S: [ _ will see _ ]; d: Denver; e: Ed; g: Georgia; s: Saturday

If the murderer is either the butler or the nephew, then I’m Sherlock Holmes

the murderer is either the butler or the nephew → I’m Sherlock Holmes

(the murderer is the butler ∨ the murderer is the nephew) → I = Sherlock Holmes

(the murderer = the butler ∨ the murderer = the nephew) → i = s

(m = b ∨ m = n) → i = s
if either m is b or m is n then i is s

b: the butler; i: I; m: the murderer; n: the nephew; s: Sherlock Holmes

Neither Ann nor Bill saw Tom speak to either Mike or Nancy

¬ (Ann saw Tom speak to either Mike or Nancy ∨ Bill saw Tom speak to either Mike or Nancy)

¬ ((Ann saw Tom speak to Mike ∨ Ann saw Tom speak to Nancy) ∨ (Bill saw Tom speak to Mike ∨ Bill saw Tom speak to Nancy))

¬ (([ _ saw _ speak to _ ] Ann Tom Mike ∨ [ _ saw _ speak to _ ] Ann Tom Nancy) ∨ ([ _ saw _ speak to _ ] Bill Tom Mike ∨ [ _ saw _ speak to _ ] Bill Tom Nancy))

¬ ((Satm ∨ Satn) ∨ (Sbtm ∨ Sbtn))
not either either S fits a, t, ən m or S fits a,t, ən n or either S fits b,t, ən m or S fits b,t, ən n

S: [ _ saw _ speak to _ ]; a: Ann; b: Bill; m: Mike; n: Nancy; t: Tom

Tom will agree if each of Ann, Bill, and Carol asks him

Tom will agree ← each of Ann, Bill, and Carol will ask Tom

Tom will agree ← ((Ann will ask Tom ∧ Bill will ask Tom) ∧ Carol will ask Tom)

[ _ will agree] Tom ← (([ _ will ask _ ] Ann Tom ∧ [ _ will ask _ ] Bill Tom) ∧ [ _ will ask _ ] Carol Tom)

Gt ← ((Aat ∧ Abt) ∧ Act)
((Aat ∧ Abt) ∧ Act) → Gt
if both both A fits a ən t and A fits b ən t and A fits c ən t then G fits t

A: [ _ will ask _ ]; G: [ _ will agree]; a: Ann; b: Bill; c: Carol; t: Tom

Reagan’s vice president was the 41st president.

Reagan’s vice president = the 41st president

[ _’s vice president] Reagan = [the _th president] 41

vr = pf
v of r is p of f

p: [the _th president]; v: [ _ ’s vice president]; f: 41; r: Reagan

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

[ _ found a fly in _ ] Tom Tom’s soup ∧ [ _ called _ ] Tom the waiter

Ft(Tom’s soup) ∧ Ctr

Ft([ _’s soup] Tom) ∧ Ctr

Ft(st) ∧ Ctr
both F fits t ən s of t and C fits t ən r

C: [ _ called _ ]; F: [ _ found a fly in _ ]; s: [ _’s soup]; r: the waiter; t: Tom

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

[ _ found _ ] Tom the book everyone had talked to Tom about ∧ [ _ bought a copy of _ ] 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([the book everyone had talked to _ about] Tom) ∧ Bt([the book everyone had talked to _ about] Tom)

Ft(bt) ∧ Bt(bt)
both F fits t ən b of t and B fits t ən b of t

B: [ _ bought a copy of _ ]; F: [ _ found _ ]; b: [the book everyone had talked to _ 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

[ _ is located in _ ] Wabash College Crawfordsville ∧ Crawfordsville = the seat of Montgomery County

Lbc ∧ c = [the seat of _ ] Montgomery County

Lbc ∧ c = sm
both L fits b ən c and c is s of m

L: [ _ is located in _ ]; s: [the seat of _ ]; b: Wabash; c: Crawfordsville; m: Montgomery County

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

[ _ and _ set _ ] Sue Tom the date of Sue and Tom’s wedding
∧ ¬ [ _ and _ decided on _ ] 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([the date of _ ] Sue and Tom’s wedding)
∧ ¬ Dst([the location of _ ] Sue and Tom’s wedding)

Sst(d(Sue and Tom’s wedding)) ∧ ¬ Dst(l(Sue and Tom’s wedding))

Sst(d([ _ and _’s wedding] Sue Tom))
∧ ¬ Dst(l([ _ and _’s wedding] Sue Tom))

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

D: [ _ and _ decided on _ ]; S: [ _ and _ set _ ]; d: [the date of _ ]; l: [the location of _ ]; w: [ _ and _ ’s wedding]; s: Sue; t: Tom

[ _ is west of _ ] Crawfordsville Indianapolis
∧ [ _ is south of _ ] Crawfordsville Lafayette

Crawfordsville is west of Indianapolis ∧ Crawfordsville is south of Lafayette

Crawfordsville is west of Indianapolis and south of Lafayette

[ _ has met _ ] Ann Bill → [ _ has met _ ] Bill Ann

Ann has met Bill → Bill has met Ann

If Ann has met Bill then he has met her

[ _ introduced _ to _ ] Alice Clarice Boris
∧ [ _ introduced _ to _ ] Alice Doris Boris

Alice introduced Clarice to Boris ∧ Alice introduced Doris to Boris

Alice introduced Clarice and Doris to Boris

[ _ wrote to _ ] Alice Boris
∧ [ _ asked _ to write _ about _ ] Alice Boris Alice Boris

Alice wrote to Boris ∧ Alice asked Boris to write Alice about Boris

Alice wrote to Boris ∧ Alice asked Boris to write her about himself

Alice wrote to Boris and asked him to write her about himself

g = c → (f = s ∧ p = t)

Green Bay = the city → (football = the sport ∧ the Packers = the team)

Green Bay is the city → (football is the sport ∧ the Packers are the team)

Green Bay is the city → football is the sport and the Packers are the team

If Green Bay is the city, then football is the sport and the Packers are the team

([ _ has spoken to _ ] Ann Bill ∧ ¬ [ _ has spoken to _ ] Ann ([ _’s father] Carol)) → ¬ Bill = [ _’s father] Carol

(Ann has spoken to Bill ∧ ¬ [ _ has spoken to _ ] 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([ _’s father] Ann)([ _’s mother] Bill) ∨ S([ _’s mother] Ann)([ _’s father] Bill)) → [ _ and _ are cross-cousins] Ann Bill

([ _ is a brother of _ ] Ann’s father Bill’s mother ∨ [ _ is a sister of _ ] 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([ _’s proposal] Bill)([ _’s proposal] Carol))
∧ Pac(m([ _’s proposal] Bill)([ _’s proposal] Carol))

Pab([the best compromise between _ and _ ] Bill’s proposal Carol’s proposal)
∧ Pac([the best compromise between _ and _ ] Bill’s proposal Carol’s proposal)

[ _ persuaded _ to accept _ ] Ann Bill the best compromise between Bill’s proposal and Carol’s proposal
∧ [ _ persuaded _ to accept _ ] 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