Recognizing and rewriting Categorical Propositions
Some Solutions
Identify and rewrite the following sentences as categorical propositions. Then translate them into QL.
1. All nudists wear clothing at meal time.
All nudists are persons who wear clothing at mealtime.
This is an A categorical proposition
Nx: x is a nudist
Cx: x is a person who wears clothing at mealtime.
(x)(Nx ⊃ Cx)
3. Each apartment has a view of the ocean.
All apartments are things with a view of the ocean.
This is an A categorical proposition
Ax: x is an apartment
Ox: x has a view of the ocean
(x)(Ax ⊃ Ox)
6. There are some who dispute about Allah and serve rebellious devils.
Some who dispute about Allah serve rebellious devils.
This is an I categorical proposition.
Dx: x disputes about Allah
Sx: x serves rebellious devils.
(∃x)(Dx & Sx)
9. Vulcans never bluff.
No Vulcans are bluffers.
This is an E categorical proposition.
Vx: x is a Vulcan
Bx: x is a bluffer
(x)(Vx ⊃ ~Bx)
12. Plenty of people see the truth but cannot attain it.
Px: x is a person
Sx: x sees the truth
Ax: x attains the truth
(∃x)(Px & (Sx & ~Ax))
15. Alcoholics are not all liquor drinkers.
Ax: x is an alcoholic
Lx: x drinks liquor
(∃x)(Ax & ~Lx)
18. Not every Frigidaire is a refrigerator.
Fx: x is a Frigidaire
Rx: x is a refrigerator
(∃x)(Fx & ~Rx)
21. Snake bites are sometimes fatal.
Sx: x is a snake bite
Fx: x is fatal
(∃x)(Sx & Fx)
24. No members except the executive committee left the room.
Mx: x is a member
Ex: x is on the executive committee
Lx: x left the room
(x)((Mx & Lx) ⊃ Ex)
27. It's not the case that some whales are not endangered.
Wx: x is a whale
Ex: x is endangered
(x)(Wx ⊃ Ex)
30. All philosophers who are neither bald nor over seven feet tall are intelligent and good looking.
Px: x is a philosopher
Bx: x is bald
Ox: x is over seven feet tall
Ix: x is intelligent
Gx: x is good looking
(x)((Px & (~Bx &~Ov)) ⊃ (Ix & Gx))
33. Not all candidates for governor are Austrian by birth, but Arnold is.
~(x)(Cx ⊃ Ax) & (Ca & Aa)
Cx: x is a candidate for governor
Ax: x is Austrian by birth
a: Arnold