course Mth 151 ю읗~Wתassignment #016
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21:48:02 `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 --> Yes, this argument is valid confidence assessment: 3
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21:48:09 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 --> OK self critique assessment: 3
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21:49:42 `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 --> If it snowed yesterday then yesterday the roads were slippery. If the roads were slippery then they were safer to drive on. So it is valid. confidence assessment: 3
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21:49:53 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 --> OK self critique assessment: 3
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21:50:28 `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 --> If it has to either rain or snow, and it did not rain, then it must have snowed. Yes, it is valid. confidence assessment: 3
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21:50:35 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 --> OK self critique assessment: 3
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21:52:11 `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 --> Yes, it's valid. If we'll have a picnic under the condition that it doesn't rain, but we don't have a picnic, then it must have rained. confidence assessment: 3
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21:52:22 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 --> OK self critique assessment: 3
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21:54:14 `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, then we'll be able to smell the wet grass: q -> r It rained yesterday: p Yesterday we were able to smell the wet grass: p -> r confidence assessment: 3
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21:54:43 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 --> OK self critique assessment: 3
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21:55:55 `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 ->r F F T T T T The statement is true. confidence assessment: 3
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21:56:22 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.
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RESPONSE --> OK self critique assessment: 3
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