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Critical Thinking Chapter 9 Operations

by: Alexis Kreusch

Critical Thinking Chapter 9 Operations PHL

Marketplace > Wright State University > PHL > Critical Thinking Chapter 9 Operations
Alexis Kreusch
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Learning how to get rid of non statements in order to be able to graph Venn Diagrams using the operations Obversion, contrapositive, and conversion and the rules to each
Critical Thinking
Jacob N. Bauer
Class Notes
critical, thinking, Chapter, 9, PHL3000-05, Jacob, Bauer




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This 5 page Class Notes was uploaded by Alexis Kreusch on Saturday October 1, 2016. The Class Notes belongs to PHL at Wright State University taught by Jacob N. Bauer in Fall 2016. Since its upload, it has received 22 views.


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Date Created: 10/01/16
9­29­16 Three Categorical Relations  Conversion, Obversion, Contrapositive  In this part of chapter nine we are faced with arguments with nons in them. These non­ items are not possible to graph on a Venn diagram. If you are asked to count non­trees  would you be able to?  o The answer is no that is the same for these arguments so we have to be able to  change the argument so that the nons disappear o In doing this we need to make sure the argument is equal to the first statement Conversion  Flipping the Subject and Predicate (First noun and second noun)  Only for E and I claims o Used with A and O will make the argument no longer equivalent  Ex. for A: All apples are fruit (Shortened: All A are F.) o Conversion: All fruit and apples (All F are A) o This is not the same shown by the diagrams  Regular Apples (A) Fruit  (F) Conversion Fruit (F) Apples (A) These two graphs are not the same for all fruit as we know are not apples.   Ex. For O: Some People are not Blondes (Some P are not B) o Conversion: Some Blondes are  not People (Some B are not P)  This makes the statements unequal Regular People (P) Blondes (B)  Conversion Blondes (B) People (P) Again these graph do not represent the same statement as the original therefore cannot use the  conversion method On the other hands E and I claims work perfectly  Ex of E: No Apples are Vegetables (No A are V) o Conversion: No Vegetables are Apples (No V are A)   This makes sense in both situations and the graphs match either way Original Apples (A) Vegetables (V) Conversion Vegetable (V) Apples (A) The graph stays the same which is same for I claims just with an X in the middle instead of it  shaded in.  Contrapositive   Only A and O  st o 1  switch the Subject and Predicate (Just like Conversion) o 2  negate the term  Apples → non­Apples  Non­Apples → Apples  Ex of A: All Apples are Fruits (All A are F) o Contrapositive: All non­Fruits and non­Apples (All non­F  are non­A)  This cannot be graphed due to the non in the statement and nons  cannot be graphed for they do not exist  Ex. Of O: Some People are not Blondes (Some P are not B) o Contrapositive: Some non­Blondes are non­people (Some  non­B are not non­P)  You might be tempted to just get rid of the double  negative but this would make the statement not  equal  Again, you can not graph this statement for the you  cannot graph anything that is non Obversion  Any claim used with this would be true (A, E, I, and O) o 1  switch it to the opposite claim (A→E, E→A, I→O, O→I) nd o 2  negate just the predicate  Ex of O: Some Students are not High Schoolers (Some S are not HS)  Obversion: 1  Some Students are High Schoolers (Some S are HS)  (Now a I claim)  2  Some Students are non­High Schoolers (Some S are non­HS) o Therefore the statement will now be equal Tips  Always define the type of claim that is being stated to figure out which operation can or  cannot be used for it o Also a way to tell if equal or not (If you use conversion with an A claim for  homework or a test and it asks if equal, one will know that is not)  Never get rid of double negatives, that can mess up the whole process  When trying to get rid of the non in a statement, there will be multiple methods and  sometimes take multiple steps to complete.   If the predicate has a non, simply use obversion to fix it  If the non is in the subject for any claim us conversion and contrapositive as appropriate.  Then use obversion to get rid of it. 


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