Deck 7: Predicate Logic Symbolization

Question 1

General theory:

-Which of the following are sentences?

A)
B)
C)
D)
E) None of these

Answer 1

Question 2

General theory:

-Which of the following are sentences?

A)
B)
C)
D)
E) None of these

Answer 2

Question 3

General theory:

-Symbolize "Some mammals are not four-legged" a) when the domain is mammals and b) when the domain is unrestricted (using obvious abbreviations).

Answer 3

a.
b.

Question 4

General theory:

-Symbolize "No whales are fish" a) when the domain is whales, and b) when the domain is unrestricted (using obvious abbreviations).

Question 5

General theory:

-What sentence contradicts "No just acts are acts that cause pain"?

A) All just acts are acts that cause pain.
B) Some just acts are acts that cause pain.
C) Some just acts are acts that do not cause pain.
D) No acts that cause pain are just acts.
E) None of these.

Question 6

General theory:

-Which sentence is equivalent to ?

A)
B)
C)
D) None of these

Question 7

General theory:

-Which sentence is equivalent to ?

A)
B)
C)
D) None of these

Question 8

Symbolize, using the indicated letters:
-No mathematician philosophers are scientists. (Mx = "x is a mathematician"; Px = "x is a philosopher"; Sx = "x is a scientist".)

Question 9

Symbolize, using the indicated letters:
-All mathematicians and philosophers are either non-philosophers or non-scientists.

Question 10

Symbolize, using the indicated letters:
-Some mathematicians and (some) philosophers are scientists.

Question 11

Symbolize, using the indicated letters:
-No one is a scientist unless he also is a mathematician and philosopher.

Question 12

Symbolize, using the indicated letters:
-Only mathematicians are scientists, and none but philosophers are mathematicians.

Question 13

Symbolize, using the indicated letters:
-No arguments that are either invalid or unsound are convincing. (Ax = "x is an argument", Vx = "x is valid"; Sx = "x is sound"; Cx = "x is convincing".)

Question 14

Symbolize, using the indicated letters:
-A student caught cheating will be expelled. (Sx = "x is a student"; Cx = "x is caught cheating"; Ex = "x will be expelled".)

Question 15

Symbolize, using the indicated letters:
-A student who was caught cheating was not expelled.

Question 16

Symbolize, using the indicated letters:
-If all students are good logicians, then they all will pass. (Sx = "x is a student"; Gx = "x is a good logician"; Px = "x will pass".)

Question 17

Symbolize, using the indicated letters:
-If a student is a good logician, then he or she will pass.

Question 18

Symbolize, using the indicated letters:
-If not all students will pass, then some students are not good logicians.

Question 19

Symbolize, using the indicated letters:
-If any students pass, then they studied hard. (Hx = "x studied hard".)

Question 20

Symbolize, using the indicated letters:
-If all students pass, then at least some of them are good logicians.

Question 21

Symbolize, using the indicated letters:
-Some students are good logicians, but are such that they won't pass unless they study hard.

Question 22

Symbolize, using the indicated letters:
-Some students are neither good logicians nor good writers, but some students are both. (Wx = "x is a good writer".)

Question 23

Translations.
Translate the following into English, being a colloquial as possible. Use same symbols as above, i.e., let Sx = "x is a student"; Cx = "x is caught cheating"; Ex = "x will be expelled"; Gx = "x is a good logician"; Px = "x will pass"; Hx = "x studied hard"; Wx = "x is a good writer"; and let Ax = "x is angry"; Yx = "x is happy"; a = Alice; b = Burt.
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Question 24

Translations.
Translate the following into English, being a colloquial as possible. Use same symbols as above, i.e., let Sx = "x is a student"; Cx = "x is caught cheating"; Ex = "x will be expelled"; Gx = "x is a good logician"; Px = "x will pass"; Hx = "x studied hard"; Wx = "x is a good writer"; and let Ax = "x is angry"; Yx = "x is happy"; a = Alice; b = Burt.
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Question 25

Translations.
Translate the following into English, being a colloquial as possible. Use same symbols as above, i.e., let Sx = "x is a student"; Cx = "x is caught cheating"; Ex = "x will be expelled"; Gx = "x is a good logician"; Px = "x will pass"; Hx = "x studied hard"; Wx = "x is a good writer"; and let Ax = "x is angry"; Yx = "x is happy"; a = Alice; b = Burt.
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Question 26

Translations.
Translate the following into English, being a colloquial as possible. Use same symbols as above, i.e., let Sx = "x is a student"; Cx = "x is caught cheating"; Ex = "x will be expelled"; Gx = "x is a good logician"; Px = "x will pass"; Hx = "x studied hard"; Wx = "x is a good writer"; and let Ax = "x is angry"; Yx = "x is happy"; a = Alice; b = Burt.
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Question 27

Translations.
Translate the following into English, being a colloquial as possible. Use same symbols as above, i.e., let Sx = "x is a student"; Cx = "x is caught cheating"; Ex = "x will be expelled"; Gx = "x is a good logician"; Px = "x will pass"; Hx = "x studied hard"; Wx = "x is a good writer"; and let Ax = "x is angry"; Yx = "x is happy"; a = Alice; b = Burt.
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Question 28

Translations.
Translate the following into English, being a colloquial as possible. Use same symbols as above, i.e., let Sx = "x is a student"; Cx = "x is caught cheating"; Ex = "x will be expelled"; Gx = "x is a good logician"; Px = "x will pass"; Hx = "x studied hard"; Wx = "x is a good writer"; and let Ax = "x is angry"; Yx = "x is happy"; a = Alice; b = Burt.
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Question 29

Translations.
Translate the following into English, being a colloquial as possible. Use same symbols as above, i.e., let Sx = "x is a student"; Cx = "x is caught cheating"; Ex = "x will be expelled"; Gx = "x is a good logician"; Px = "x will pass"; Hx = "x studied hard"; Wx = "x is a good writer"; and let Ax = "x is angry"; Yx = "x is happy"; a = Alice; b = Burt.

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