course Mth 151 ~яpvgxassignment #016
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16:39:12 `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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RESPONSE --> Valid because if you are able to smell the grass when it rains and it rained, then you can smell the grass. confidence assessment: 2
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16:40:07 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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RESPONSE --> Since we could smell the grass when it rained you would be able to smell the grass yesterday when it did rain. self critique assessment: 2
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16:42:26 `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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RESPONSE --> It would be valid because it states that if it snows the roads get slippery and slippery roads are safer to drive on. Since it snowed, the roads would be safe. It doesn't have to be true to valid. confidence assessment: 2
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16:44:07 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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RESPONSE --> Even though you want to say it is invalid because our common sence tells us its not, it doesn't have to be true to valid. self critique assessment: 2
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16:45:32 `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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RESPONSE --> Valid because the first statement says it will rain or snow and since it didn't rain it snowed. confidence assessment: 2
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16:46:21 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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RESPONSE --> The statement said it would do one or the other so it had to do one, either rain or snow. self critique assessment: 2
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16:48:05 `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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RESPONSE --> Valid because it said that if it didn't rain they would have a picnic, they didn't have their picnic so it must have rained. confidence assessment: 2
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16:49:05 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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RESPONSE --> The statement said they would picnic if it didn't rain and since they didn't get to have their picnic it must have rain. self critique assessment: 2
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16:55:05 `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' and 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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RESPONSE --> If the grass gets wet, we'll be able to smell it. q -> r; it rained, the grass got wet and we were able to smell the grass (p ^ q) ^r confidence assessment: 1
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16:56:36 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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RESPONSE --> I knew that I would use p q r but I wasn't sure how to place them in order or how to put them all together, I didn't break the sentences. self critique assessment: 2
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17:02:26 `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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RESPONSE --> p q r (p->q) (q->r) (p->q)^(q->r)^p->r F F T T T T confidence assessment: 2
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17:08:12 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 true 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.
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RESPONSE --> I got the right answer but I am confused when I went over your explanation. I am confused on the q->r is false since q is false and p is false but won't you compare q & r instead of q & p. I am confused as to why it is q & r. self critique assessment: 2
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