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Translate each of the following arguments into symbolic form using the variables given below. D = The drought will continue. S = We get an early...
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Translate each of the following arguments into symbolic form using the variables given below.
D = The drought will continue.
S = We get an early storm.
M = Managers of the ski areas will be happy.
F = There will be great fire danger next year.
Match the correct translation for the argument to the lettered options given below.
(You will get the most out of this exersize if you do translations for all five arguments before looking at the answer choices.)
_____ 1. The drought will continue if we don’t get a storm. If we do get a storm, the managers of the ski areas will be happy. Since we’ll either get a storm or we won’t, it follows that either the drought will continue or the ski area managers will be happy.
_____ 2. Unless an early storm moves in, the drought will continue, and there will be great danger of fire next year. But the drought is not going to continue. Therefore, there will not be a great danger of fire next year.
_____ 3. If there’s no early storm, the drought will continue. If the drought continues, there will be a great danger of fire next year. So, if there is to be no great danger of fire next year, there must be an early storm.
_____ 4. There will be a great danger of fire next year only if the drought continues, and it will continue unless we get an early storm. However, if we do get an early storm, the ski area managers will be happy. So if the ski area managers are not happy, it’ll mean that there’s going to be a great danger of fire next year.
_____ 5. Either there will be an early storm, or the drought will continue. If there’s no continuation of the drought, then the managers of the ski areas will be happy and there will be no great danger of fire next year. So if we’re both to avoid any great danger of fire next year and to make the ski area managers happy, it will be necessary for there to be an early storm.
………………………………………..
[a] S v (D & F) alternatively ~S ® (D & F)
~D ~D
____ ____
~F ~F
[b] S v D
~D ® (M & ~F)
____
(F & M) ® S
[c] ~S ® D
D ® F
____
~F ® S
[d] (F ® D) & (D v S) alternatively (F ® D) & (~S ® D)
S ® M S ® M
____ ____
~M ® F ~M ® F
[e] ~S ® D S ® M
S v ~S ____
D v M
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Part 2: Construct a truth table for each of the following arguments. Use the grids provided and fill in the correct values Indicate whether each argument is valid or invalid.
In your homework responses, all you need to do is say whether each argument is valid or invalid.
