Ann introduced Bill to Carol

[λxyz (x introduced y to z)] Ann Bill Carol

Iabc
I fits a, b, ’n c

Ann gave the book to either Bill or Carol

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

[λxyz (x gave y to z)] Ann the book Bill ∨ [λxyz (x gave y to z)] Ann the book Carol

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

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

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

[λxyz (x gave y to z)] Ann the book Bill ∧ [λxyz (x gave y to z)] Bill the book Carol

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

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

[λxyz (x had y sent to z)] Tom the package Sue ∧ [λxy (x was returned to y)] the package Tom

Htps ∧ Rpt
both H fits t, p, ’n s and R fits p ’n t

Georgia will see Ed if she gets to Denver before Saturday

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

[λxy (x will see y)] Georgia Ed ← [λxyz (x will get to y before z)] Georgia Denver Saturday

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

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

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))

¬ (([λxyz (x saw y speak to z)] Ann Tom Mike ∨ [λxyz (x saw y speak to z)] Ann Tom Nancy) ∨ ([λxyz (x saw y speak to z)] Bill Tom Mike ∨ [λxyz (x saw y speak to z)] Bill Tom Nancy))

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

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)

[λx (x will agree)] Tom ← (([λxy (x will ask y)] Ann Tom ∧ [λxy (x will ask y)] Bill Tom) ∧ [λxy (x will ask y)] Carol Tom)

Gt ← ((Aat ∧ Abt) ∧ Act)
((Aat ∧ Abt) ∧ Act) → Gt
if both both A fits a ’n t and A fits b ’n t and A fits c ’n t then G fits t

[λxy (x is west of y)] Crawfordsville Indianapolis
∧ [λxy (x is south of y)] Crawfordsville Lafayette

Crawfordsville is west of Indianapolis ∧ Crawfordsville is south of Lafayette

Crawfordsville is west of Indianapolis and south of Lafayette

[λxyz (x introduced y to z)] Alice Clarice Boris
∧ [λxyz (x introduced y to z)] Alice Doris Boris

Alice introduced Clarice to Boris ∧ Alice introduced Doris to Boris

Alice introduced Clarice and Doris to Boris

[λxy (x wrote to y)] Alice Boris
∧ [λxyzw (x asked y to write z about w)] 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