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LOGICAL REASONING

FOR

CAT 2009

LOGICAL DEDUCTIONSLOGICAL DEDUCTIONS

Logical PremisesLogical Premises

All As are Bs

Premise

Quantifier

Subject Predicate

Venn DiagramsVenn Diagrams

All As are BsNo A is B

B A

B

A

Venn DiagramsVenn DiagramsSome As are Not

BsSome As are

Bs

B A

B A

A B

B

A

A

B

B

A

A B

QUANTIFIERSQUANTIFIERS

Basic Quantifie

rPremise

Quantifier

Subject Predicate

AllAffirmativ

eUniversal

No Negative Universal

SomeAffirmativ

eParticular

Some Not Negative Particular

RulesRulesThe middle term must not appear

in the conclusion

◦All As are Bs ◦All Bs are Cs

◦Conclusion cannot contain B

Middle Term

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.

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

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

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.

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.

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

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.

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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