Deck 10: Relational Predicate Logic

Question 1

Symbolizing
-If something is heavy, then Art won't lift it. (Hx = "x is heavy"; a = "Art"; Lxy = "x will lift y".)

Answer 1

Question 2

Symbolizing
-If something is heavy, then anyone who is weak will not lift it. (Px = "x is a person"; Wx = "x is weak".)

Answer 2

Question 3

Symbolizing
-Everyone who loves himself hates someone (or other). (Px = "x is a person"; Lxy = "x loves y"; Hxy = "x hates y".)

Answer 3

Question 4

Symbolizing
-All who have sinned have come short of the glory of God. (Px = "x is a person"; Sx = "x has sinned"; Cxy = "x has come short of y"; g = "the glory of God.")

Question 5

Symbolizing
-If anything is heavy, then there is something heavier than this piece of chalk, which happens not to be heavy. (Hx = "x is heavy"; Hxy = "x is heavier than y"; c = "this piece of chalk".)

Question 6

Symbolizing
-All freshmen date only seniors. (Fx = "x is a freshman"; Dxy = "x dates y"; Sx = "x is a senior".)

Question 7

Symbolizing
-Some freshmen date only seniors.

Question 8

Symbolizing
-Some freshmen date every senior.

Question 9

Symbolizing
-Some freshmen date no seniors.

Question 10

Symbolizing
-No freshmen date all seniors.

Question 11

Symbolizing
-No freshmen date any seniors.

Question 12

Symbolizing
-Not all freshmen date seniors.

Question 13

Symbolizing
-Not all freshmen date every senior.

Question 14

Symbolizing
-Jones will listen to Smith, even though Smith is boring. (j = "Jones"; s = "Smith"; Lxy = "x will listen to y"; Bx = "x is boring".)

Question 15

Symbolizing
-All sinners who sin against someone who is a sinner are sinned against by someone who is a sinner. (Sx = "x is a sinner"; Sxy = "x sins against y".)

Question 16

Symbolizing
-If every sinner is sinned against by everyone who is a sinner, then everyone who sins against someone (or other) sins against himself.

Question 17

Symbolizing
-Someone who is a sinner and sins against someone (or other) who is a sinner sins against himself.

Question 18

Symbolizing
-All heads of horses are heads of animals, provided that all horses are animals. (Hx = "x is a horse"; Ax = "x is an animal"; Hxy = "x is the head of y".)

Question 19

Translations.
Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage):
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Question 20

Translations.
Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage):
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Question 21

Translations.
Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage):
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Question 22

Translations.
Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage):
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Question 23

Translations.
Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage):
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Question 24

Translations.
Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage):
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Question 25

Translations.
Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage):
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Question 26

Translations.
Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage):
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Question 27

Translations.
Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage):
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Question 28

Translations.
Letting Hxy = "x is heavier than y", translate the following into English (coming as close as possible to colloquial usage):
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Question 29

Proving invalidity.
Show that the following arguments are invalid:
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Question 30

Proving invalidity.
Show that the following arguments are invalid:
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Question 31

Prove valid

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Question 32

Prove valid
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Question 33

Prove valid
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Question 34

Prove valid

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Question 35

Theorems of logic.
Prove that the following are theorems of logic:
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Question 36

Theorems of logic.
Prove that the following are theorems of logic:
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Question 37

Theorems of logic.
Prove that the following are theorems of logic:
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Question 38

Theorems of logic.
Prove that the following are theorems of logic:

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