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II. CHAPTER TWO: SYMBOLIZING IN SENTENTIAL LOGIC
A. General Theory
For 1-3, circle one of a-d:
1. A compound sentence is truth functional if and only if:
a. the truth value of the compound sentence is determined by the truth values of
its component sentences
b. each of its component sentences is either true or false
c. the truth values of the component sentences are determined by the truth values
of the compound
d. none of these
2. The sentence “It will rain only if the temperature drops” is correctly symbolized
(using obvious abbreviations) as:
a. R D
b. D R
c. R D
d. none of these
3. The sentence “It will rain unless the temperature drops” is correctly symbolized (using
obvious abbreviations) as:
a. R D
b. D R
c. R D
d. none of these
4. a. Give an original example of a truth functional use of a sentence connective in
ordinary English, and defend your view that it is truth functional.
b. Give an original example of a non truth functional use of a sentence connective in
ordinary English, and defend your view that it is non truth-functional.
For 5 and 6, identify the main connective.
5. ~[(A B) (B C)] (F G)
6. ~[~G (B A)]
A. Answers
1. a
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B. Symbolizing
Symbolize the following, letting R= “It will rain”, U= “The temperature will go up”, D
= “The temperature goes down”, S= “It will snow”:
1. It won’t snow, unless the temperature goes down.
2. The temperature will go up only if it doesn’t rain, and will go down if it does rain.
3. The temperature will go down just in case it rains.
4. The temperature will go up or down but not both.
5. If it neither snows nor rains, the temperature won’t go up and it won’t go down.
6. Either it snows and the temperature won’t go up, or it rains and the temperature
won’t go down.
7. If it rains, then if the temperature goes down it will snow.
8. If it rains, then it snows if and only if the temperature goes down.
9. It won’t rain, but it will snow unless the temperature goes up.
10. If it rains, the temperature will go up unless, of course, it goes down.
11. It will snow if and only if it does not rain and the temperature does not go up.
12. If it both rains and snows, then the temperature is neither going up nor going
down.
B. Answers (Note that you may accept sentences logically equivalent to these)
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C. Translating
Translate the following into more or less colloquial English sentences. Let J= “Art gets
a new job”; B= “Art gets a new boss”; A= “Art gets a new apartment”; R= “Art get a
new roommate.”
1. ~ (J B) 4. ~ J~ [(B (A R)]
2. J (B A) 5. (~ A~R) ~ J
3. ~ (A R) 6. (B J) (R A)
C. Answers
1. Art will get neither a new job nor a new boss.