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