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LOGICAL REASONING
FOR
CAT 2009
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LOGICAL DEDUCTIONSLOGICAL DEDUCTIONS
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Logical PremisesLogical Premises
All As are Bs
Premise
Quantifier
Subject Predicate
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Venn DiagramsVenn Diagrams
All As are BsNo A is B
B A
B
A
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Venn DiagramsVenn DiagramsSome As are Not
BsSome As are
Bs
B A
B A
A B
B
A
A
B
B
A
A B
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QUANTIFIERSQUANTIFIERS
Basic Quantifie
rPremise
Quantifier
Subject Predicate
AllAffirmativ
eUniversal
No Negative Universal
SomeAffirmativ
eParticular
Some Not Negative Particular
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RulesRulesThe middle term must not appear
in the conclusion
◦All As are Bs ◦All Bs are Cs
◦Conclusion cannot contain B
Middle Term
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RulesRulesWhen both premises are
affirmative, conclusion cannot be negative
All As are BsSome Bs are Cs
Then, conclusion should have only All or Some as the quantifier.
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RulesRules
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
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RulesRulesThe middle term must be
distributed at least once.
◦All As are Bs , Some Bs are Cs
◦All As are Bs, Some As are Cs
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RulesRulesIf one of the premises is
particular, then conclusion is particular
Some Bs are CsAll Cs are Ds
Conclusion has to have quantifier as some.
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RulesRulesWhen One Quantifier is negative,
the conclusion must be negative
No As are BsAll Bs are Cs
Conclusion must have quantifier as some not or No.
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RulesRulesA 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
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Lets Try an Example 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.
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SolutionSolution
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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THANK YOUTHANK YOU
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