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Slide 2 http://nov15.wordpress.com LOGICAL REASONING FOR CAT 2009 Slide 3 LOGICAL DEDUCTIONS Slide 4 Logical Premises All As are Bs Premise Quantifier Subject Predicate Slide 5 Venn Diagrams All As are Bs No A is B B A B A Slide 6 Venn Diagrams Some As are Not Bs Some As are Bs B A B A A B B A A B B A A B Slide 7 QUANTIFIERS Basic Quantifier PremiseQuantifierSubjectPredicate AllAffirmativeUniversal NoNegativeUniversal SomeAffirmativeParticular Some NotNegativeParticular Slide 8 Rules The middle term must not appear in the conclusion All As are Bs All Bs are Cs Conclusion cannot contain B Middle Term Slide 9 Rules When both premises are affirmative, conclusion cannot be negative All As are Bs Some Bs are Cs Then, conclusion should have only All or Some as the quantifier. Slide 10 Rules There must be 3 and only 3 distinct terms When both premises are particular no conclusion can be derived Some + some not, some + some, etc When both premises are negative, no conclusion can be derived No + no, no + some not, some not + some not Slide 11 Rules The middle term must be distributed at least once. All As are Bs, Some Bs are Cs All As are Bs, Some As are Cs Slide 12 Rules If one of the premises is particular, then conclusion is particular Some Bs are Cs All Cs are Ds Conclusion has to have quantifier as some. Slide 13 Rules When One Quantifier is negative, the conclusion must be negative No As are Bs All Bs are Cs Conclusion must have quantifier as some not or No. Slide 14 Rules A term which isnt distributed in the premise should not be distributed in the conclusion. All As are Bs All Bs are Cs --------------------- Middle Term All As are Cs Some A/Cs are C/As Slide 15 Lets Try an Example You say that sappy movies are always bad? I can prove that isn't true. For instance, Steven Spielberg always makes great movies! But some of his movies are sappy. So, some sappy movies are also great. Slide 16 Solution All Steven Speilberg movies are Great Some Steven Speilberg movies are sappy Answer is and particular Some Sappy movies are Great Slide 17 THANK YOU http://nov15.wordpress.com