PREDICATE LOGIC IN CLASS EXERCISES

 

Symbolize the following simple non-relational statements (e.g., Ms “Socrates is mortal”).

 

(1) Joe is a consultant Cj

(2) Claire is a skydiver Sc

 

Symbolize the following compound non-relational statements (contains logical connectives, e.g., ~Vh “Hitler was not virtuous”).

 

(3) Bob is not a thief ~Tb

(4) Joe is happy if and only if Bob is sad Hj ↔ Sb

(5) Claire is eavesdropping or Bob is eavesdropping Ec v Eb

 

Symbolize the following two-place relational predicates (e.g., Lbc “Bob loves Claire”).

 

(6) Claire shops at Kohls Sck

(7) Joe does not shop at Walmart ~Sjw

(8) If Claire shops at Kohls or Joe shops at Walmart, then Bob shops at Goodies (Sck v Sjw) → Sbg

 

 

Symbolize the following three-place relational predicates (e.g., Gcfb “Claire gave Fido to Bob”).

 

(9) Claire spilled water on Joe Scwj

(10) Claire spilled water on herself Scwc

(11) If Claire spills water on Bob, then Bob will spill water on Claire Scwb → Sbwc

 

Complete and symbolize the following symmetrical, asymmetrical, or nonsymmetrical relationships.

 

(12) Joe is handcuffed to Bob  Hjb → Hbj (symmetrical)

(13) Joe was born before Claire Bjc → ~Bcj (asymmetrical)

 

Complete and symbolize the following transitive, intransitive or nontransitive relationships.

 

(14) Claire is faster than Joe and Joe is faster than Bob (Fcj &Fjb) → Fcb (transitive)

(15) Claire emails Joe and Joe emails Bob (Ecj &Ejb) → (Ecb v ~Ecb) (nontransitive)

 

Symbolize the following non-relational quantification statements.

 

(16) Some sponges are not purple Ǝx(Sx & ~Px)

(17) All sponges are porous x(Sx → Px)

(18) Not everything is a sponge ~x(Sx)

 

Symbolize the following relational quantification statement.

 

(19) No partiers like the masked-keg-chugger x(Px → ~Lxm)

 

Symbolize the following identity predicates.

 

(20) Bob is the masked-keg-chugger b=m or  Ǝx[Mx & y(My → y=x) & x=b]

(21) There are at least two spies in this room  ƎxƎy[(Sx & Sy) & ~x=y]

(22) Bob is the ugliest person in this room Pb & x[(Px & ~x=b) → Ubx]