MODEL ANSWERS FOR PREDTRAN

Note: put a blank on either side of ‘v’ when it is used to mean “or”, rather than a variable.

Problem Set 1

(1) Lac : Alfred loves Claudia

(2) Laa : Alfred loves himself

(3) (x)(Dx > Ux) : All dogs are ugly

(4) (Ex)(Dx & Ux) : Some dogs are ugly

(5) (Ex)Lax : Alfred loves something

(6) (x)Lxa : Everything loves Alfred

(7) (Ex)Lxx : Something loves itself

(8) (x)~Lxx : Nothing loves itself

(9) (Ex)((Dx & Ux) & ~Cx) : Some ugly dogs are not cats

(10) ((Ex)(Dx & Nx) & (Ey)(Cy & ~Ny)) : Some dogs run and some cats don't

(11) (x)((Sx & Cx) > ~(Ox & Dx)) : No strange cat is a nosey dog

(12) (Ex)(Dx & (Ox & Ux)) : Some dogs are nosey and ugly

(13) (x)((Dx v Cx)>(Ox & Ux)) : All dogs and cats are nosey and ugly

(14) (x)(Gx > Lxa) : Every logician loves Alfred

(15) (x)(Gx > Rdx) : Every logician is resented by Dagmar

(16) (Ex)(Lxc & Rxe) : Something loves Claudia and resents Eva

(17) ((Ex)Lxc & (Ey)Rye) : Something loves Claudia and something resents Eva

(18) (x)((Ux & Gx) > ~Ldx) : No ugly logicians are loved by Dagmar

(19) (x)(Gx > Rxb) > Rab : If every logician resents Bart then so does Alfred

(20) (Ex)(Gx & ((y)(Dy > Rxy) & (Ez)(Cz & Lxz))) : Some logician who resents all dogs loves some cat

Problem Set 2

(1) Ocn : California overlaps North America

(2) Pnc : North America is part of California

(3) ~Odc : Delaware doesn't overlap California

(4) (x)(Oxs > Oxc) : Whatever overlaps San Diego overlaps California

(5) (x)(y)(Pxy > Oxy) : Every part of a thing overlaps that thing

(6) (Onc & ~Pnc) : North America overlaps California, but is not part of it

(7) (x)(Pxc > ~Pxd) : No part of California is part of Delaware

(8) (x)(Ey)(Oxy & ~Pxy) : Everything overlaps something it isn't part of

(9) (Ex)(Pxo & ~Pxc) : Some part of the Universe is not part of California

(10) (Pcn ≡ (x)(Oxc > Oxn)) : California is part of North America if and only everything that overlaps California overlaps North America

(11) (x)(Pxo > (Ey)(Gy & Hyx)) : Every part of the Universe is hated by some logician

(12) (x)(y)(Oxy > Oyx) : Everything that overlaps a thing is overlapped by that thing

(13) (x)((~Oxx v ~Pxx) > Tx) : Everything that doesn't overlap itself or is not part of itself is abstract

(14) (x)((Gx&Oxc) > Nx) : Every logician who overlaps California runs

(15) (x)((Ey)(Pyo & Pxy) > Pxo) : Every part of a part of the Universe is a part of the Universe

(16) (x)((Tx & Gx) > (y)(Hyc > Hyx)) : All abstract logician are hated by all who hate California

(17) (x)(((Gx & Hxs) & ~Hxc) > ~Hxd) : Logicians who hate San Diego but not California don't hate Delaware either

(18) (x)((Ey)((Ty & Gy) & Hxy) > (Ez)((Nz & Gz) & Hxz)) : Anything which hates an abstract logician hates a logician who runs

(19) (x)(Tx > ~(Ey)(Pxy & Gy)) : Nothing abstract is part of any logician

(20) (x)((Pxn & ~(Oxd v Oxc)) > ~(Ey)(Gy & Oxy)) : No part of North America that overlaps neither Delaware nor California overlaps any logicians BUG: The computer may not accept the right answer on this one