#$&* course mth151 nov 3rd 016. `query 16
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Given Solution: `a** You would put all dogs in a circle, and this circle would be inside another circle consisting of all things that love to bury bones. Archie is outside this bone-burying circle and since this circle contains all dogs Archie isn't a dog. This makes the argument valid. The x for Archie has to go outside the outer circle, so it has to be outside the inner circle. Thus the x can't be in the inner circle, and Archie therefore can't be a dog. The conclusion can't be contradicted. COMMON ERROR WITH INSTRUCTOR RESPONSE: I put 'all dogs like to bury bones' in one circle and 'archie likes to bury bones' in another. INSTRUCTOR RESPONSE: You don't want to use a single circle to represent a compound statement. 'All dogs like to bury bones' and 'Archie likes to bury bones' are compound statements. SIMILAR ERROR: in one circle ,I put all dogs love to bury bones, inthe other circle I put Archie, so I knew that Archie wasn't a dog, so the statement is valid . INSTRUCTOR COMMENT: See previous comment. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `qquery 3.5.20 all chickens have a beak. All hens are chickens. Therefore all hens have beaks. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: this would be valid sayings all hens have beaks confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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). ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `qWhen 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. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: the circles would connect and would say both chickens and hens have beaks. confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** The circle for hens must be inside the circle for chickens, which is inside the circle for beaked creatures. Therefore the circle for hens must be inside the circle for beaked creatures. No other way to draw it consistent with the conditions. ** &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary): ------------------------------------------------ Self-critique Rating: ********************************************* Question: `q(formerly 3.5.27). The text 'dumbed down' the problems in this section. This question is a bit challenging but is similar in nature to assigned problems: Using Venn diagrams evaluate the following argument:{}{}All drivers contribute to traffic congestion. All contributors to traffic congestion make life a little worse. Some people who live in the suburbs make life a little worse. Therefore some people who contribute to traffic congestion live in the suburbs. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: it would contradict because it doesn't specify the overlapping part confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: ********************************************* Question: `q(formerly 3.5.27). The text 'dumbed down' the problems in this section. This question is a bit challenging but is similar in nature to assigned problems: Using Venn diagrams evaluate the following argument:{}{}All drivers contribute to traffic congestion. All contributors to traffic congestion make life a little worse. Some people who live in the suburbs make life a little worse. Therefore some people who contribute to traffic congestion live in the suburbs. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: it would contradict because it doesn't specify the overlapping part confidence rating #$&*: 3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: `a** 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. " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!