LOGICAL REASONING FOR CAT 2009

LOGICAL DEDUCTIONS

Logical Premises All As are Bs Premise Quantifier Subject Predicate

Venn Diagrams All As are Bs No A is B B A B A

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

QUANTIFIERS Basic Quantifier PremiseQuantifierSubjectPredicate AllAffirmativeUniversal NoNegativeUniversal SomeAffirmativeParticular Some NotNegativeParticular

Rules The middle term must not appear in the conclusion ◦ All As are Bs ◦ All Bs are Cs ◦ Conclusion cannot contain B Middle Term

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.

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

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

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.

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.

Rules A term which isn’t 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

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.

Solution All Steven Speilberg movies are Great Some Steven Speilberg movies are sappy Answer is and particular Some Sappy movies are Great

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