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21:00:31 `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 --> I think this argument is valid becuase all the premises are true. I came to this conclusion by using the Venn Diagram.
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21:00:45 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
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21:04:11 `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 --> Even though this argument makes no logical sense, I think that it is a vaild argument because it states that snow makes roads slippery and slippery roads are safer to drive on. The conclusion agrees with this argument making it valid.
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21:04:42 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
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21:07:45 `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 --> I think that this argument is valid because it states that ""today, it will rain or it will snow."" And since it also states that it didn't rain, then it must have snowed because it says it will do one or the other.
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21:08:02 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. I got this one right.
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21:09:01 `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 --> I think this argument is valid because I assume that since we didn't have a picnic, then it must have rained based on the specifics of the argument.
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21:09:18 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. I got this one right.
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21:13:52 `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 the wet grass. q -> r It rained yesterday. p Therefore, we were able to smell the wet grass. r (p -> r)
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21:17:50 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, I didn't symbolize the whole complex statement. I understand how it is put together here with the ^ symbols meaning 'and' however, I'm not confident that I could put it in this form using the brackets just yet. I do understand completely what you have given here though.
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21:20:41 `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 -->
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21:28:18 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 --> oopps! I didn't mean to click 'enter response', sorry. Ok, I had this right up until I got to the q -> r statement. In my truth table, I had this one as true. I am a little confused with this answer you have given here though. I think my mistake started with the q -> r statement.
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$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ hhܮۦPzZ̯Ʃ⊽ assignment #016 g}ၳQ} Liberal Arts Mathematics I 12-07-2005
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21:32:40 query 3.5.6 all dogs love to bury bones. Archie doesn't. Therefore Archie isn't a dog .
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RESPONSE --> I think this argument is valid because it states that all dogs love to bury bones. And since Archie doesn't love to bury bones, he is not a dog. I came to this conclusion because for Archie to be a dog, he would have to love to bury bones.
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21:34:15 ** You would put all dogs in a circle, and this circle would be inside another circle consisting of all things that love to bury bones. Archie is outside this bone-burying circle and since this circle contains all dogs Archie isn't a dog. This makes the argument valid. The x for Archie has to go outside the outer circle, so it has to be outside the inner circle. Thus the x can't be in the inner circle, and Archie therefore can't be a dog. The conclusion can't be contradicted. COMMON ERROR WITH INSTRUCTOR RESPONSE: I put 'all dogs like to bury bones' in one circle and 'archie likes to bury bones' in another. INSTRUCTOR RESPONSE: You don't want to use a single circle to represent a compound statement. 'All dogs like to bury bones' and 'Archie likes to bury bones' are compound statements. SIMILAR ERROR: in one circle ,I put all dogs love to bury bones, inthe other circle I put Archie, so I knew that Archie wasn't a dog, so the statement is valid . INSTRUCTOR COMMENT: See previous comment.
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RESPONSE --> Ok. I got this one right. I almost made the common error though of using one circle for a compound statement.
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21:36:04 query 3.5.20 all chickens have a beak. All hens are chickens. Therefore all hens have beaks.
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RESPONSE --> This is a valid argument. I used a large circle for things with beaks. Inside this circle, I had another circle for chickens. Inside this circle, I had circle for hens. Therefore, all hens have beaks.
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21:36:51 ** You need to show the relationship between chickens and things with breaks. You would make a circle for everything with a beak and another circle for chickens. Since all chickens have beaks the chicken circle has to be inside the 'beaked' circle. Then you have hens. They are all chickens so the hen circle is inside the chicken circle. Since the chicken circle is already inside the beaked circle the hen circle (inside the chicken circle) is also inside the beaked circle, and you conclude that all hens have beaks. COMMON ERROR WITH INSTRUCTOR COMMENT: In the outer circle, I put chickens with beaks. Inside that circle, I made another circle for hens are chickens. INSTRUCTOR COMMENT: 'hens are chickens' is a statement, not a thing. The circles have to be defined by things. SIMILAR ERROR WITH COMMENT: Two circles: large circle of hens are chickens and a smalled circle within of hens have beaks. Valid INSTRUCTOR COMMENT: You don't put propositions into circle (e.g., 'hens are chickens' isn't a circle). You put sets of things into circles (e.g., a circle for hens and a circle for chickens, with the hens circle inside the chickens circle). **
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RESPONSE --> I got this one right.
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21:39:29 When the diagram is drawn according to the premises, is it or is it not possible for the diagram to be drawn so that it contradicts the conclusion? If it is possible describe how.
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RESPONSE --> I don't think that it can be drawn so that it contradicts the conclusion because the statements are very specific as to what they are describing.
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21:39:45 ** The circle for hens must be inside the circle for chickens, which is inside the circle for beaked creatures. Therefore the circle for hens must be inside the circle for beaked creatures. No other way to draw it consistent with the conditions. **
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RESPONSE --> Ok, I got this one right.
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21:47:28 3.5 27 all drivers contribute. All contributors make life a little worse. Some people in the suburbs make life a little worse. Therefore some people who contribute live in the suburbs.
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RESPONSE --> I think that this argument is invalid becuase my diagram did not prove that all people who live in the suburbs contribute to air pollution.
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21:49:42 ** BRIEF SOLUTION: Drivers circle inside contributors circle. Contributors circle inside make-life-worse circle. Suburbs circle overlaps make-worse circle but the degree of overlap is not specified, and the circle doesn't necessarily extend all the way into the contributors circle. So the picture can be drawn to contradict the conclusion without contradicting the given premises. WITH A LITTLE MORE DETAIL: You would have circles for drivers, contributors, people who make life worse and people in the suburbs. All drivers contribute so the drivers circle would be inside the contributors circle. All contributors make life worse so their circle would be inside the 'people who make life worse' circle. The people-in-the-suburbs circle has to be inside the make-life-worse circle. The make-life-worse circle contains the other two circles, and there is a place in that circle for the people-in-suburbs circle such that the people-in-suburbs circle doesn't intersect any of the other circles (put it in the part of the make-life-worse circle that doesn't contain either of the other two circles). So it's possible to put all people in the suburbs outside of the 'contribute' circle. COMMON SENSE: In commonsense terms, which you should relate to the picture, nothing is said that forces all people in the suburbs into the drivers circle or the contributors circle, since the statement is that SOME people in the suburbs make life worse. There might be a little old lady in the suburbs who doesn't drive and does nothing but make life better--this is not contradicted by the 'some people in suburbs make things worse' statement. Thus the argument is invalid. COMMON ERROR WITH COMMENTARY: all drivers contribute goes in one circle. All contributors make life a little worse goes in another. Some people in the suburbs make life a little worse goes in a third. INSTRUCTOR COMMENT Again classes of things, not relationships, go into the circles. Everything you listed here is a relationship, not a class of objects. **
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RESPONSE --> OK, I didn't have my diagram exactly like you have described here. I had the contributer circle on the outside. I should have had the makes live worse circle on the outside. I understans what you have described here.
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