Examination Questions And Answers English Work Sheet Page 4
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73. d
4. a. The word “and” in the sentence “Art went to the show and Betsy went to the show”
is truth−functional, because the truth value of the sentence formed by this connective is a
function of the truth value of the two conjuncts, “Art went to the show” and “Betsy went
to the show”.
b. The word “because” in the sentence “Art went to the show because Betsy went to the
show” is not truth−functional. For example the sentence may be false if both component
sentences are true or it may be false. In other words, the truth value of the sentence is not
a function of its component parts.
5. The horseshoe.
6. The first tilde.
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)
~ D ⊃ ~ S
R ⊃ (D ⊃ S)
1.
7.
(U ⊃ ~ R) ⋅ (R ⊃ D)
R ⊃ (S ≡ D)
2.
8.
D ≡ R
~R ⋅ (~U ⊃ S)
3.
9.
(U ∨ D) ⋅ ~ (U ⋅ D)
R ⊃ (~ D ⊃ U)
4.
10.
~ (S ∨ R) ⊃ (~ U ⋅ ~ D)
S ≡ (~ R ⋅ ~ U)
5.
11.
(S ⋅ ~ U ) ∨ (R ⋅ ~ D)
(R ⋅ S) ⊃ ~ (U ∨ D)
6.
12.
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