7 Tips for Solving Reasoning Questions on Logical Deduction

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Tip #1: Validity of statements after Conversion

The conversion operation moves the subject term to the predicate term position, and moves the predicate term to the subject term position.

1.    Statement: All S are P (Applicable for Case 1, 2 and 6)

Converse: All P are S

Validity: NO

(Not true for Case 2 and 3)

2.    Statement: No S are P (Applicable for Case 5)

Converse: No P are S

Validity: YES

3.    Statement: Some S are P (Applicable for Case 1, 2, 3, 4, 6 and 7)

Converse: Some P are S

Validity: YES

4.    Statement: Some S are not P (Applicable for Case 3, 4, 5 and 7)

Converse: Some P are not S

Validity: NO

(Not true for Case 3 and 7)

Tip #2: Validity of statements after Obversion

The obversion operation is performed by changing the quality of the statement and replacing the predicate with its complement (Refer to figures above)

1.    Statement: All S are P (Applicable for Case 1, 2 and 6)

Obverse: No S are non-P

Validity: YES

2.    Statement: No S are P (Applicable for Case 5)

Obverse: All S are non-P

Validity: YES

3.    Statement: Some S are P (Applicable for Case 1, 2, 3, 4, 6 and 7)

Obverse: Some S are not non-P

Validity: YES

4.    Statement: Some S are not P (Applicable for Case 3, 4, 5 and 7)

Obverse: Some S are non-P

Validity: YES

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Tip #3: Validity of statements after Contraposition

Like conversion, contraposition switches the subject and predicate. Then, it replaces the two terms with their complements. (Refer to figures above)

1.    Statement: All S are P (Applicable for Case 1, 2 and 6)

Converse: All non-P are non-S

Validity: YES

2.    Statement: No S are P (Applicable for Case 5)

Converse: No non-P are non-S

Validity: NO

(Not true for Case 5)

3.    Statement: Some S are P (Applicable for Case 1, 2, 3, 4, 6 and 7)

Converse: Some non-P are non-S

Validity: NO

(Not true for Case 6 and 7)

4.    Statement: Some S are not P (Applicable for Case 3, 4, 5 and 7)

Converse: Some non-P are not non-S

Validity: YES

Tip #4: Rules to eliminate conclusions from premises

1.    If one premise is negative, the conclusion must be negative.

Statements: (I) All grasses are trees.    (II) No tree is shrub.

Conclusions: (I) No grasses are shrubs. (II) Some shrubs are grasses.

Since 1 premise is negative, the conclusion must be negative.

Conclusion II cannot follow.

2.    If one premise is particular (using ‘some’), the conclusion must be particular.

Statements: (I) some girls are thieves. (II) All thieves are dacoits.

Conclusions: (I) some girls are dacoits. (II) All dacoits are girls.

Since 1 premise is particular, conclusion must be particular.

Conclusion II cannot follow.

3.    If both the premises are positive, the conclusion must be positive.

Statements: (I) All women are mothers. (II) All mothers are sisters.

Conclusions: (I) All women are sisters.  (II) Some women are not sisters.

Both premises are positive, so conclusion must be positive.

Conclusion II cannot follow.

4.    If both the premises are universal (using ‘all’ or ‘no’), the conclusion must be universal.

Statements: (I) All men are fathers.   (II) All fathers are brothers.

Conclusions: (I) All men are brothers. (II) Some men are not brothers.

Both premises are universal, so conclusion must be universal.

Conclusion II cannot follow.

Tip #5: Cases where no conclusions can be derived

1.     If a term is not found in the premises, no conclusion related to that term can be made.

For example, consider the following statement and conclusion.

Statement: Some kings are queens.

Conclusion: All kings are beautiful.

Since the term ‘Kings’ has not been distributed in the premise, it cannot be distributed in the conclusion. Hence conclusion cannot follow.

2.     No conclusion follows if both premises are particular.

Statements: (I) some books are pens. (II) Some pens are erasers.

Conclusions: (I) All books are erasers.  (II) Some erasers are books.

Both the premises here are particular. Thus, no conclusion can follow.

3.     No conclusion follows if both premises are negative.

Statements: (I) No flower is mango. (II) No mango is cherry.

Conclusions: (I) No flower is cherry.  (II)Some cherries are mangoes.

Since both the premises are negative, no conclusion follows.

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Tip #6: If the conclusion are mutually exhaustive, then one of them must follow

Statements: Bureaucrats marry only intelligent girls. Tania is very intelligent.

Conclusions: (I) Tania will marry a bureaucrat. (II) Tania will not marry a bureaucrat.

A.   Only conclusion I follows    

B.   Only conclusion II follows

C.   Either I or II follows           

D.   Neither I nor II follows

E.    Both I and II follow

Solution:

There is no middle term and nothing is said about Tania's marriage in the premises. But, the two conclusions are complementary, so one of them must follow.

Hence, the correct answer is C.

Tip #7: Use Venn Diagrams where suitable

Statements: All benches are desks.  Some desks are roads.  All roads are pillars.

Conclusions: (I) some pillars are benches. (II) Some pillars are desks. (III) Some roads are benches. (IV) No pillar is bench.

A.   A. None follows                  

B.   Only either I or IV, and III follow

C.   Only either I or IV follows              

D.   Only either I or IV, and II follow

E.    All follow

Solution:

Any of these 3 are possible. From the Venn Diagrams, it is clear that: Some pillars are desks, so conclusion II follows. Roads does not overlap with Benches. So III will not follow. Now, Pillars may or may not intersect with benches. So, either I or IV will follow. Thus, the correct answer will be D.

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