LOGICAL REASONING

In logical reasoning one draws inferences or conclusions from statements or premises and
test the validity of such inferences. The following terms are useful in understanding the
principles of logical reasoning.
Proposition : A proposition is a statement of a relationship between two terms.
A categorical statement to be in standard form, the sentence expressing that statement
must begin with quantifier such as all!, no!, some!. It must then present the sub"ect
term # the term designating the set of ob"ects the statements is about $ followed by copula
# either are! or are not! # followed by the predicative term.
%uantifier & sub"ect & copula & predicative term.
A # All graduates are literates.
' # (o graduates are criminals.
I $ )ome graduates are businessmen.
* # )ome graduates are not rich people.
)tatement A $ +niversal affirmative
)tatement ' $ +niversal negative
)tatement I $ Particular affirmative
)tatement * $ Particular negative
Distribution of terms
A term is distributed in such a sentence if it refers to all members of the set of ob"ects
denoted by the term, otherwise it is said to be undistributed.
'x : , All graduates are literates.
)ub"ect graduates # distributed
-iterate $ undistributed.
'x : . (o graduates are criminals.
)ub"ect / predicate distributed.
'x : 0 )ome graduates are businessmen.
(either sub"ect nor predicate distributed.
'x : 1 )ome graduates are not rich people.
*nly predicate distributed.
2ollowing are the rules used in solving logical reasoning.
3ule , : If both propositions are particular or one affirmative and one negative or both
affirmative, the inference will be uncertain.
)ome graduates are businessmen.
)ome graduates are honest
)ome honest persons are businessmen.
The inference is uncertain.
3ule . : If one premise is negative, the inference must be negative. If the inference is
universal affirmative, it is definitely false. 4ut, if it is particular affirmative inference will be
correct. 4ecause, that will be the implication of the particular negative proposition.
All men are graduates.
)ome rice people are not graduates.
)o all rich people are men.
)ome rich people are men.
3ule 0 : In a categorical argument there must be a middle term. If there is no middle term
no inference can be derived.
All birds fly
(o human being flies
)o, no human being is a bird.
Inference is incorrect.
5y hand touches the chair
The chair touches the ground.
5y hand touches the ground.
Inference is incorrect.
3ule 1 : The middle term must be distributed at least once in the premises, otherwise
inference is uncertain.
All chairs are furniture.
All tables are furniture.
)o all tables are chairs.
5iddle term furniture is undistributed.
3ule 6 : If a middle term is distributed in the inference, it must be distributed in the ma"or
premise, otherwise the inference is false.
All chairs are pens.
(o table is a boo7.
)o, no table is a chair.
3ule 8 : If a minor term is distributed in the inference it must be distributed in the ma"or
premise, otherwise inference will be false.
(o horse is dog.
All dogs are rats.
)o, no rat is a horse.
Inference is false.
Exercise :
9irections : Two statements are followed by . possible inferences. :ou have to point out
which of the following answer choices applies to each of the following questions :
a; *nly inference I is followed.
b; *nly inference II is followed.
c; 4oth inference I / II are followed.
d; (either inference I nor II followed.
1. All horses are on!e"s. All on!e"s are mon!e"s.
i) All horses are mon7eys.
ii) All mon7eys are horses
#. No rice is foo$ No foo is brea.
i; (o bread is rice
iii) (o rice is bread
ii;
0. All %a%ers are boo!s$ Some %a%ers are files.
i; )ome files are boo7s
iv) )ome boo7s are files
ii;
&. Some %ens are boo!s$ No %encil is a rubber.
i; )ome rubbers are not boo7s
v) )ome boo7s are not rubbers.
ii;
'. No cro( is a s%arro($ All hens are ea)les.
i; (o eagle is a sparrow
ii; (o sparrow is a eagle.
Directions : Choose the best alternati*e.
8. <e cannot vote because he is a minor.
a; )ome minors cannot vote in elections.
b; )ome who cannot vote are minors.
c; (o minor can vote.
d; All minors cannot vote.
=. No businessman is )oo because all businessmen are cheat.
a; (o businessman is cheat.
b; All good are not cheat.
c; (o good person is cheat.
d; All cheat are not good.
>. +e is (ise because all )rauates are (ise.
a; <e is a graduate.
b; <e is not a graduate.
c; )ome graduates are he
d; )ome graduates are not he.
,. Aso!a (as %o%ular$ because he (as fair.
a; All popular are fair
b; All fair are popular
c; *nly fair are popular
d; (one.
1-. +e cannot rea$ because he is a blin.
a; (o blind can read.
b; All blind cannot read
c; All who can read are not blind
d; )ome who read are not blind.
11. +e (ear turban$ so he is a si!h.
a; All who wear turban are )i7hs
b; All )i7hs wear turban.
c; *nly )i7hs wear turban
d; )ome )i7hs wear turban.
1#. +e (ears s(eater$ because he is sic!.
a; All who wear sweater are sic7.
b; All sic7 wear sweater
c; (o sic7 wear sweater
d; All sic7 do not wear sweater.
1.. /ic! %oc!ets are hate$ because the" are criminals.
a; All who are hated are pic7 poc7ets.
b; All criminals are hated.
c; All hated are criminals.
d; )ome criminals are hated.
1&. +e is unha%%"$ because he has faile in exam.
a; All unhappy fails.
b; )ome who fail are unhappy.
c; )ome unhappy fails.
d; All who fails, are unhappy.
1'. +e li*e lon)$ because he (as health".
a; All who lived long are healthy.
b; All healthy live long.
c; (o healthy live long.
d; )ome healthy live long.
9irections : An interrogative sentence is followed by . arguments. *ne beginning with
yes! and the other beginning with no!. :ou are to pic7 one of the following answer
choices which is applicable to each of the following questions :
A. *nly argument , is forceful.
4. *nly argument . is forceful.
?. 4oth arguments are forceful.
9. (either , nor . is forceful.
10. +as Inia been consistentl" non1ali)ne2
1. :es. 4ecause India has not sided with any big power.
2. (o. 4ecause India did not condemn 3ussian occupation of Afganistan.

13. Shoul eucation be 4ob oriente2
,. :es. 4ecause purpose of education is to prepare us for earning.
.. (o. because education should not be for the sa7e of education.

15. Shoul Inia remain secular2
,. :es. 4ecause people belonging to different religions live in India.
.. (o. 4ecause the different religious group do not see eye to eye
with one another.

1,. Shoul stri!es be banne in essential ser*ices2
,. :es. 4ecause stri7e disturbs the normal life.
.. (o. 4ecause it is a democratic right of the people.

#-. In Inia$ shoul income tax be abolishe2
,. :es, because it is an unnecessary burden on the wage earners.
.. (o, because it is a good source of revenue.

#1. 6ar!in) o)s ne*er bite.
,. 9ogs always bite.
.. )ome dogs bite.

##. 7an is born free.
,. 2reedom is the birth right of man.
.. The very birth confirms right on man.

#.. I %ra" to )o (hene*er I am in ifficult".
,. Prayers can solve problems.
.. Prayers to god is the highest duty of man.

#&. Lau)h$ an the (orl (ill lau)h (ith "ou.
,. People generally laugh.
.. -aughter symboli@es happiness.

#'. O(in) to stress$ "ou i)esti*e s"stem is affecte.
,. There is a stress in life.
.. 9igestive system has no defensive.

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