course Mth 151
If your solution to stated problem does not match the given solution, you should self-critique per instructions at
http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm
.
Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.
016. Translating Arguments
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `q001. There are 6 questions in this set.
Is the following argument valid?
'If it rains, the grass will get wet.
If the grass gets wet, we'll be able to smell the wet grass.
It rained yesterday.
Therefore yesterday we were able to smell the wet grass.'
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Your solution:
This is valid
I believe you understand why this is valid; be aware that on a test you would have to fully explain why the argument is valid. There are only two possible answers, and you would have a 50-50 chance of picking the right one even if you didn't know; so this sort of thing must be explained.
Confidence Assessment:
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Given Solution:
This argument certainly seems valid. We say what will happen if rains, and what will happen is that happens. Then we say that it rains, so the whole chain of happenings, rained then wet grass then smell, should follow.
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `q002. Is the following argument valid:
'If it snows, the roads will be slippery.
If the roads are slippery they'll be safer to drive on.
Yesterday it snowed.
Therefore yesterday the roads were safer to drive on.'
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Your solution:
I would say this is a fallacy because roads are not safer if the road is slippery but being that I have no other premise to go on it must be valid.
Confidence Assessment:
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Given Solution:
The validity of an argument has nothing to do with whether the statements in that argument are true or not. All we are allowed to do is assume that the statements are indeed true, and see if the conclusions of the argument therefore hold. In this case, we might well question the statement 'if the roads are slippery they'll be safer to drive on', which certainly seems untrue. However that has nothing to do with the validity of the argument itself. We can later choose to reject the conclusion because it is based on a faulty assumption, but we cannot say that the argument is invalid because of a faulty assumption.
This argument tells us that something will happen if it snows, and then tells us what we can conclude from that. It then tells us that it snows, and everything follows logically along a transitive chain, starting from from the first thing.
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Self-critique (if necessary):
&#Your response did not agree with the given solution in all details, and you should therefore have addressed the discrepancy with a full self-critique, detailing the discrepancy and demonstrating exactly what you do and do not understand about the given solution, and if necessary asking specific questions (to which I will respond).
&#
Self-critique Rating:
Question: **** `q003. Is the following argument valid:
'Today it will rain or it will snow.
Today it didn't rain.
Therefore today it snowed.'
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Your solution:
Well it says it will rain or snow and since it didn’t rain then it must have snowed so I would say valid.
Confidence Assessment:
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Given Solution:
If we accept the fact that it will do one thing or another, then at least one of those things must happen. If it is known that if one of those things fails to happen, then, the other must. Therefore this argument is valid.
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `q004. Is the following argument valid:
'If it doesn't rain we'll have a picnic.
We don't have a picnic.
Therefore it rained.'
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Your solution:
It says they will be a picnic if it doesn’t rain so they didn’t have a picnic it must have rained making this valid.
Confidence Assessment:
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Given Solution:
In this argument where told the something must happen as a result of a certain condition. That thing is not happen, so the condition cannot have been satisfied. The condition was that it doesn't rain; since this condition cannot have been satisfied that it must have rained. The argument is valid.
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Self-critique (if necessary):
&#This also requires a self-critique.
&#
Self-critique Rating:
Question: **** `q005. We can symbolize the following argument:
'If it rains, the grass gets wet.
If the grass gets wet, we'll be able to smell the wet grass.
It rained yesterday.
Therefore yesterday we were able to smell the wet grass.'
Let p stand for 'It rains',
q for 'the grass gets wet'
r for 'we can smell the wet grass'.
Then the first sentence forms a compound statement which we symbolize as p -> q. Symbolize the remaining statements in the argument.
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Your solution:
p->q
q->r
p^r
Confidence Assessment:
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Given Solution:
The argument gives three conditions, 'If it rains, the grass gets wet. If the grass gets wet, we'll be able to smell the wet grass. It rained yesterday.', which are symbolized p -> q, q -> r and p. It says that under these three conditions, the statement r, 'we can smell the wet grass', must be true. Therefore the argument can be symbolized by the complex statement
[ (p -> q) ^ (q -> r) ^ p] -> r.
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Self-critique (if necessary):
I didn’t conjucted them together.
You also missed the -> . However you made a good start, and you were close.
Self-critique Rating:
Question: **** `q006. The preceding argument was symbolized as [ (p -> q) ^ (q -> r) ^ p] -> r. Determine whether this statement is true for p, q, r truth values F F T.
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Your solution:
p q r p->q q->r ^p ->r
T T T T T T
T T F T F F
T F T F T F
T F F F T F
F T T T T T
F T F T F F
F F T T T T
F F F T T T
I think I am way off.
A little short, but not that far off.
Confidence Assessment:
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Given Solution:
For these truth values p -> q is true since p is false (recall that the only way p -> q can be false is for p to be true and q to be false), q -> r is false since q is false, and p itself is false, therefore [ (p -> q) ^ (q -> r) ^ p] is false. This makes [ (p -> q) ^ (q -> r) ^ p] -> r true, since the statement can only be false if [ (p -> q) ^ (q -> r) ^ p] is true while r is false.
I see the truth value is already given so I need to just prove why it is.
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