applicationsof logical reasoning - university of … philosophy - vi sem. additional... ·...

APPLICATIONS OF

LOGICAL REASONING

VI SEMESTER

ADDITIONAL COURSE(In lieu of Project)

BA PHILOSOPHY

(2011 Admission)

UNIVERSITY OF CALICUT

SCHOOL OF DISTANCE EDUCATION

Calicut university P.O, Malappuram Kerala, India 673 635.

School of Distance Education

Applications of Logical Reasoning 2

UNIVERSITY OF CALICUT

SCHOOL OF DISTANCE EDUCATION

STUDY MATERIAL

Additional Course (In lieu of Project)

BA PHILOSOPHY

VI Semester

APPLICATIONS OF LOGICAL REASINING

Prepared &

Scrutinized by:

Dr. V. Prabhakaran,Sreevisakh,Thekkegramma Road,Sastha Nagar, Chittur.

Layout: Computer Section, SDE

©Reserved



CONTENTS PAGE No

MODULE I 4

MODULE II 11

MODULE III 14

MODULE IV 17

MODULE V 22



Aims and objectives:1. To develop the student’s critical thinking and intellectual problem-solvingcapability.2. To test the ability of the student to apply the theory and solve problemsinvolving tests of reasoning.3. To develop skill for linguistic analysis and the ability to detect errors inreasoning.

MODULE IREDUCTION OF ORDINARY LANGUAGE SENTENCES INTO

STANDARD FORM SENTENCES.

The traditional logic recognized four forms of propositions(A, E , I , O). Aproposition which is not expressed in one of these forms is to be reduced toone of these according to the meaning of the proposition.

Categorical propositions are classified with regard to quality andquantity: From the point of view of quality categorical propositions are eitheraffirmative or negative.

An Affirmative proposition is one in which an agreement is affirmedbetween the Subject and Predicate, or in which the Predicate is asserted of theSubject , e.g. snow is white. A Negative proposition is one which the Predicateis denied of the Subject. It indicates a lack of agreement between the Subjectand Predicate. E.g. The room is not cold.

The quantity of a proposition is determined by the extension of theSubject . on the basis of quantity categorical propositions are either universalor particular.

A universal proposition is one in which the Predicate refers to all theindividual objects denoted by the Subject . (the subjects is taken in its fullextension) E.g. All men

2

are rational. A particular propositions is one in which the Predicate belongsonly to a part of the denotation of the subject. E.g. some metals are white.

Particular propositions usually begin with some word or phrase showingthat the subject is limited in extent. The logical sign of particular proposition is“some”, but other qualifying words or phrases, such as “the greatestpart”, ‘nearly all’, ‘several’, ‘a small number’, ‘a few’, etc. also indicateparticularity.



A.E.I.O. Combining quantity and quality we get four types of categoricalpropositions, Universal Affirmative,Universal Negative,ParticularAffirmative,Particular Negative.. A.E.I.O. are used to symbolise themA and I from affirmo stand for ‘affirmative’ propositions; E and O, thevowels from ‘Nego’ for negative propositions.

The four types of propositions are:

Universal affirmative: It is a categorical proposition in which thepredicate agrees with the whole subject, e.g. All men are rational.

All S is P

Universal negative proposition: It is a categorical proposition inwhich the predicate does not at all agree with any part of the subject.E.g. No men are perfect.

No S is P

particular affirmative proposition: is a categorical proposition inwhich the predicate agrees only with a part of the subject. E.g. someflowers are red.

Some S is P

particular negative proposition is a categorical proposition inwhich the P does not agree with a part of the S. e.g. some Indians arenot religious.

Some S is not P

S = Subject; P = Predicate

The purpose of reducing sentences to logical form is to make the meaning ofthe sentence clear in logical reasoning. If propositions are stated in their logicalform, testing of inferences becomes easier.

3

The points to be remembered in changing sentences to logical form are:

1.The meaning of the original proposition is to be preserve in the standardform proposition.

2.The proposition must contain all the three parts in he proper order, subject,copula and predicate.

3. A suitable copula must be used between the subject and the predicate.

4. The sign of negation must go with the copula, and not with the predicate.



5. Compound sentences must be split up into simple propositions.

6. The quantity and quality of the proposition must be decided and statedclearly.

The following procedure is to be followed while reducing propositions totheir logical form:

Subject and predicate of the given proposition are to be identified. Subject isthat about which the assertion is made. Predicate is that which is asserted ofthe subject.

Having identified the subject and predicate , the quality of the proposition isto be known, affirmative or negative whether the predicate is affirmed ordenied of the subject.

Next, the quantity of the proposition is to be known. If the predicate is affirmedor denied of the entire denotation of the subject, the proposition is Universal. Ifthe predicate is affirmed or denied of a part of the denotation of the subject,the proposition is Particular.

Certain general rules are to be followed :

*Sentences which have words like ‘all’, ‘every’ , each ,any, whoever, with thesubject and words like always, necessarily with the predicate are to bereduced into A form.

Every ticket-holder must be admitted.

L.F: All ticket-holders are persons who must be admitted.

Any man can do that

L.F: All men are persons who can do that.

4

Any criminal is punishable

L.F: All criminals are punishable.

Poets always love nature.

L.F: All poets are lovers of nature.

Virtues are absolutely desirable.

L.F: All virtues are desirable.

*Sentences with all, every, any etc containing the signof negation , not are tobe reduced to O form.

All that glitters is not gold



L.F: Some things that glitters are not gold.

Every disease is not fatal

L.F: Some diseases are not fatal

Any fruit is not sweet

L.F: Some fruits are not sweet

Not every good bowler is a good batsman.

L.F: Some good bowlers are not good batsmen

Every cloud does not bring rain

L.F: Some clouds are not those which bring rain

*Sentences with no, none, never, nothing, nobody, not one, not a single, are tobe reduced to E proposition.

Not a single student has passed

L.F: No student is one who has passed.

Nothing done in hurry is well done.

L.F: No acts done ina hurry are acts which are well done.

5

Not one was saved in the shipwreck

L.F: No sailors are those who were saved in wreck

Misers are never happy

L.F: No misers are happy.

No lazy man succeeds in life.

No lazy men are successful.

None can live for ever

L.F: No persons are those who can live for ever

*Sentences containing words as some, most, a few, mostly, generally, all butone, almost all, frequently, often, many, certain, nearly all, a small number,the majority, sometimes, nearly always are to be reduced to the particular( Ior O).

Girls are generally shy

L.F: Some girls are shy

Many a flower is born to blush unseen



L.F: Some flowers are things born to blush unseen

Most Hindus are vegetarians

L.F; Some Hindus are vegetarians

Many rules are easy

L.F: Some rules are easy

A few students do not work hard

L.F: Some students are not those who work hard

Most of the students are not hostellers

L.F: Some students not hostellers

*Sentences containing words as few, seldom, hardly.

6

, scarcely, are to be reduced to O if there is no sign of negation and to I ifthere is a sign of negation.

Few men are reliable

L.F: Some men are reliable

Few men have not suffered disappointments in life

L.F: Some men are those who have suffered disappointments in life

Students seldom pass this examination in the first attempt

L.F: Some students are not those who pass this examination in the firstattempt

*Singular proposition is reduced to a Universal proposition when the singularsubject is a definite individual or a collection of individuals. If the subject is anindefinite singular term,the singular proposition should be taken as aParticular proposition.

Gandhiji is the Father of Indian Nation.- A

The sky is blue.-A

One minister is not rich

L.F: Some ministers are not rich

*Indefinite or indesignate propositions are treated as Universal when thepredicate is an invariable and common attribute of the subject.



*Indefinite propositionsare treated as Particular when predicate is only anaccidental quality.

Glass is breakable

L.F: All glasses are breakable.

Material bodies gravitate

L.F: All material bodies are things which gravitate.

Lemons are not apples.

L.F: No lemons are apples

Catholics are Christians

7

All Catholics are Christians

Indians are poor

L.F: Some Indians are poor

Trains are not punctual

L.F: Some trains are not punctual

*Sentences containing words as except, all but, save, called exceptivepropositions are to be reduced to Universal if the exceptions are definitelyspecified. If the exceptions are indefinite, the exceptive sentences are reducedto Particular propositions.

All students except Shyam have passed

L.F: All students except Shyam are those who have passed

No students except Shyam have failed

L.F: No students except Shyamare those who have failed

All students except two have passed

L.F: Some students are those who have passed

No students except two have passed

L.F: Some students are not those who have passed

All but James passed

L.F: All persons other than James are persons who passed

All but a few were saved

L.F: Some persons are those who were saved



All metals except one are solid

L.F: Some metals are solid.

*Exclusive sentences containing words as alone, only, none but, none exceptno one else but, nothing but are reduced to E proposition. By contradicting theoriginal subject and used as the

8

subject of the logical proposition. Exclusive sentences may also be changedinto Universal propositions by inter-changing the original subject andpredicate.

None but citizens can hold property.

L.F: No non-citizens are persons who cn hold property.

Or

All those who can hold property are citizens

Only the wise are fit to rule

L.F: No non-wise persons are fit to rule

Or

All persons fit to rule are wise

Graduates alone can vote

L.F: No non-graduates are voters

Or

All voters are graduates

*Where the quantity of the proposition is not explicit, it is the meaning of thesentence that must be taken into account in reducing to the logical form .

To be wise is to be happy

L.F: All wise people are happy

To err is human

L.F: All cases of erring are human

Blessed are the pure

L.F: All pure persons are blessed

There are bright colours

L.F: Some colours are bright

9



MODULE IIConversion of A, E ,I, O propositions according to relations ofopposition between categorical propositions as shown in the traditionalsquare of opposition.

IMMEDIATE INFERENCE

Inference is a mental process of drawing something new from somethingknown.

Mediate inference consists in drawing a new proposition from two knownpropositions. The mediate inference asserts the agreement or disagreement of asubject and predicate after having compared each with a common element ormiddle term. The conclusion is thus reached mediately or indirectly. There aretwo kinds of immediate inferences: Opposition and Eduction.

Traditional logic considers opposition of propositions as a system of inferences.Traditionally opposition deals with inferences within the four-fold scheme ofpropositions. Opposition of propositions is a scheme of inferences between twopropositions which have the same subject and the same predicate , but differeither in quantity or in quality or both in quantity and quality.

There are four kinds of logical opposition, contrary opposition, contradictoryopposition, sub-contrary opposition, and sub-altern opposition.

1. Contrary Opposition or contrariety: is the relation between twouniversal propositions having the same S and P but differing in quality only.A and E

E.g. All A is B--. No A is B.

All misers are unhappy.----No miser is unhappy.

2. Contradictory opposition is the relation between two propositionshaving the same S and P but differing both in quality and quantity. Iand O; I and E

A and O

E.g. All boys are clever-some boys are not clever.

10

I and E

Some boys are clever- No boys are clever.

3. Subcontrary opposition or subcontrariety: is the relation betweentwo particular propositions having the same S and P but differing inquality only. I and O



E.g. Some able men are honest.

Some able men are not honest.

4. Subaltern opposition or subalternation: is the relation betweentwo

propositions having the same S and P but differing in quantity only. In

subalternation the universal is called subalternant and thecorresponding particular is called subalternate. A and I : E and O

All men are mortal - Some men are mortal.

No men are mortal- Some men are not mortal.

As an immediate inference opposition consists in drawing out from thetruth or falsity of a given proposition the truth or falsity of its logical oppositehaving the same subject and predicate but differing in quality only or inquantity only or in both.

Laws of Oppositional Inference

1. Law of Contrary Opposition

Between contraries if one is true the other s false, and if one is false theother is doubtful. Contrary propositions cannot both be true, but both may befalse.

All men are rational T

No men are rational F

No students are industrious F

All students are industrious-undetermined

11

2. Law of Contradictory Opposition

If one of the contradictories is rue the other must be false; if one is falsethe other must be true. Both can neither be true or false at the same time.

No men are perfect T/F

Some men are perfect T/F

3. Law of Subcontrary Opposition

Between subcontraries if one is false the other is necessarily true; but ifone is true the other is doubtful. Both may be true; both cannot be false.



Some men are angels F

Some men are not angles T

Some students are honest T

Some students are not…undetermined

Some fruits are sweet T

Some fruits are not sweet T

4. Law of Subalternation

Between subalterns if the universal is true the corresponding particularis also true; but if the universal is false the particular is doubtful.

E.g. No gamblers are honest T

Some gamblers are not honest T

All students are clever F

Some students are clever--undetermined

If the particular proposition is true its corresponding universal isdoubtful; but if the particular is false the universal must be false.

12

Some politicians are not honest T

No politicians are honest--undetermined

Some men are not rational F

No men are rational F



MODULE IIIChanging categorical propositions into converse, obverse, andcontrapositive according to rules of eduction/immediate inference.

Conversion, Obversion, Contraposition and Inversion are immediateinferences.

Conversion

Conversion is an immediate inference in which from a given propositionanother proposition having the original predicat as the new subject , and theoriginal subject as the new predicat but expressing the same meaning as thatof the given proposition. The proposition to be converted is called theconvertend and the converted proposition is called the converse. It is a processby which from a proposition of the form S-P a proposition of the form P-S isinferred. Conversion expresses the same idea by interchanging the subjectand predicate.

Rules of conversion:

Term undistributed in the convertend not be distributed in the converse.

Keep the same quality

Interchange subject and predicate

Two types of conversion, simple conversion and conversion by limitation

Simple conversion---quantity and quality not changed

Conversion of E and I

No Hindus are Muslms- convertend

13

No Muslims are Hindus-- Converse

Conversion by limitation—quantity changed

Conversion of A:

All tigers are animals(convertend)

Some animals are tigers(converse)

O proposition has no converse. The subject undistributed in the convertendbecome distributed in the converse. This would go against the rule ofdistribution.



Obversion

Obversion is an immediate inference in which from a given proposition a newproposition is inferred which has the original subject as subject and thecontradictory of the original predicate as it’s predicate. The quality of theproposition is also changed. The original proposition is called obvertand andthe inferred proposition is called the obverse.

Obvertend obverse

A--All tigers are animals E—No tigers are non-animals

E—No liers are honest A—All liers are non-honest

I—Some students are sportsmen O—Some students are not non-sportsmen

O—Some men are not lazy I—Some men are non-lazy

Contraposition

Contraposition is an immediate inference in which from a given propositionanother proposition having the contradictory of the given predicate as it’ssubject is inferred.

There are two forms of contraposition, partial and full. When the predicate ofthe contrapositive is the same as the original subject, it is partialcontraposition. When the predicate of the inferred proposition is also thecontradictory of the original subject, it is full contraposition.

14

To get the contrapositive, first obvert and then convert the obverse.

Contraposition of A:

All tigers are animals

No tigers are non-animals (obverse)

No non-animals are tigers (partial contrapositive)

All non-animals are non-tigers (full contrapositive)

Contraposition of E:

No liers are reliable

All liers are non-reliable(obverse)

Some non-reliable persons are liers (partial contrapositive)

Some non-reliable persons are not non-liers (full contrapositive)



Contraposition of I:

Some metals are heavy

Some metals are not non-heavy (obverse)

Some non-heavy things are not metals (no converse, hence no contrapositive)

I proposition has no contrapositive

Contraposition of O:

Some politicians are not honest

Some politicians are non-honest (obverse)

Some non-honest persons are politicians (partial contrapositive)

Some non-honest persons are not non-politicians (full contrapositive).

15



MODULE IVDetecting fallacies according to the rules of categorical syllogism.

CATEGORICAL SYLLOGISM

Definition of Syllogism

A Syllogism is a form of mediate deductive inference, in which the conclusionis drawn from two premises, taken jointly. It is a form of deductive inferenceand therefore the conclusion cannot be more general than the premises. It is amediate form of inference because the conclusion is drawn from two premises,and not from one premise only as in the case of immediate inference.

Eg : All men are mortal

All kings are men

.` . All kings are mortal.

Structure of Syllogism

A syllogism consists of three terms. The predicate of the conclusion iscalled the Major Term; subject of the conclusion is called the Minor Term; andthat term which occurs in both the premises, but does not occur in theconclusion, is called the Middle Term. The Major and Minor terms are calledExtremes, to distinguish them from the Middle term.

The Middle Term occurs in both the premises, and is the commonelement between them. The conclusion seeks to establish a relation betweenthe Extremes—the major term and the minor term. The middle term performsthe function of an intermediary. The middle term is thus “middle” in the sensethat it is a mediating term, or a common standard of reference, with which twoother terms are compared and is thus means by which we pass from premisesto conclusion. The middle term having performed its function of bringing theextremes together drops out from the conclusion. Thus, we reach theconclusion in a Syllogism, not directly or immediately, but by means theMiddle term.

16

The premise in which the major term occurs is called the Major Premise andthe premise in which the minor term occurs is called the Minor Premise, Forexample, in the following Syllogism:

All men are mortal

All kings are men

.`. All kings are mortal.



The term ‘mortal’ is the major term, being the predicate of theconclusion; the term `kings` is minor term, because it is the subject of theconclusion; the term `men` which occurs in both the premises but is absentfrom the conclusion, is the middle term. The first premise Àll men are mortalìs the major premise, because the major term `mortal` occurs in it; the secondpremise Àll kings are men` is the minor premise, because the minor term`kings’ occurs in it .

It may be pointed out that when a syllogism is given in strict logical form,the major premise is given first, and the minor premise comes next, and last ofall comes the conclusion. The symbol M stands for the Middle term, S standsfor the Minor term and P stands for the Major term. The above syllogism canbe represented as,\

All M is P

All S is M

.`. All S is P

General Rules of Categorical Syllogism and the Fallacies.

I. Every syllogism must contain three, and only three termsand these terms must be used in the same sense throughout.

There are two ways in which this rule is violated. If a syllogism consists of 4terms instead of three, we commit the fallacy of 4 terms quartenio-terminorum e.g.

The book is on the table

The table is on the floor

.`.The book is on the floor

17

Here there are four terms, viz., “The book”, “on the table,” “The table” and “onthe floor.” Hence no conclusion can follow.

There is another way in which the above rule can be violated. If any term in asyllogism is used ambiguously in the two different premises, we commit afallacy. If a term is use in two different meanings, it is practically equivalent totwo terms and the syllogism commits the fallacy of equivocation. There arethree forms of equivocation. They are:

1.Fallacy of ambiguous major

2.Fallacy of ambiguous minor

3.Fallacy of ambiguous middle



1.Fallacy of ambiguous major is a fallacy which occurs when a syllogismuses its major terms in one sense in the premise and in a differentsense in the conclusion.

e.g., Light is required for taking a photograph.

Feather is not required for taking a photograph

.`. Feather is not light.

‘Light’ in the major premise is used in the sense of ‘physical phenomenon’ ; inthe conclusion it is used in the sense of ‘not heavy’

2.The fallacy of ambiguous minor occurs when in a syllogism the minorterm means one thing in the minor premise and quite another in theconclusion.

e.g., No boys are part of a book.

All pages are boys.

.`.No pages are part of a book.

In this syllogism, minor term ‘pages’ mean ‘boy servant’ in its premiseand the ‘side of a paper’ in the conclusion. Hence the fallacy of ambiguousminor.

3.The fallacy of ambiguous middle will be committed by a syllogism if ituses the middle term in one sense in the major premise and in anothersense in the major premise and in another sense in the minor premise.

e.g.,All criminal actions ought to be punished by law

18

prosecutions for theft are criminal actions

.`.. prosecutions for theft ought to be punished by law

The middle term ‘criminal actions’ means ‘crimes’ in the major premiseand an ‘action against a criminal’ in the minor premise. Hence thesyllogism commits the fallacy of ambiguous middle.

II. Every syllogism must contain 3 and only 3 propositions.

Syllogism is a process of reasoning in which a conclusion is drawn fromtwo given premises. Two propositions are given ad a third one is inferred.

III.The middle term must be distributed at least once in the premises.

The function of a middle term in a syllogism is to serve as the connectinglink between the minor and major terms. In the major premise P is



compared with M and in the minor premise S is compared with the sameM. thus the relation between S and P is established through themediation of M.

The violation of this rule leads to the fallacy of undistributed middle.

e.g., All donkeys are mortal.

All monkeys are mortal.

.`.All monkeys are donkeys.

In this argument the middle term ‘mortal’ is undistributed in both thepremises as the predicate of an affirmative proposition. Hence the fallacy ofundistributed middle occurs.

IV. No term which is undistributed in the premises can be distributedin the conclusion.

This rule guards us against inferring more in the conclusion than whatis contained in the premises. In any syllogism, the conclusion cannot be moregeneral than the premises.

The violation of this rule would result in two fallacies illicit major andillicit minor. The fallacy of illicit major occurs when the major term which isnot disturbed in the major premise is distributed in the conclusion.

19

e.g. All men are selfish MAP

No apes are men SEM

.`.No apes are selfish SEP

The major term ‘selfish’ is undistributed in the major premise butdistributed in the conclusion. Hence the fallacy of illicit major.

The fallacy of illicit minor is one which occurs when the minor term isdistributed in the conclusion without being distributed in the minor premise.

e.g. All thugs are murderers MAP

All thugs are Indians MAS

.`.All Indians are murderers SAP

Here the minor term ‘Indians’ is distributed in the conclusion withoutbeing distributed in the minor premise. So it commits the fallacy of illicitminor.



V. From two negative premises, no conclusion is possible.

We cannot draw any conclusion from two negative premises. For, themajor premise being negative, the major term does not agree with M. in theminor premise also, the minor term has no relation with M. Thus there is nomediating link between S and P. In the absence of a common link between Sand P, no relation can be established between them.

The violation of this rule commits the fallacy of two negative premises.

e.g. No monkeys are rational

No men are monkeys.

No conclusion is possible

VI. If one premise is negative, the conclusion must be negative andif the conclusion is negative one premise must be negative.

20

If one premise is negative the other premise must be negative. In thenegative premise ‘M’ does not agree with the other term. In the affirmativepremise ‘M’ agrees with the other term. Hence in mediating between the twoterms, ‘M’ can establish only a relation of disagreement between S and P in theconclusion. In other words the conclusion must be negative.

VII. Two particular premises yield no valid conclusion.

This is proved by examining the four possible combinations of twoparticular premises.

I O I O

I I O O

X X X X

VIII. If any one premise is particular the conclusion must be particular.



MODULE VDeriving the logical conclusion from two given premises.

Logic deals with the question of validity of arguments. Logic is the science ofthe valid forms of reasoning. The study of logic contributes towards forming acritical habit of mind which has it’s own value. The task of logic is to clarify thenature of the relationship which holds between premises and conclusion in avalid argument. To infer means to recognize what is implied in the premises. Ifwe recognize that the conclusion is implied in the premises , then we can saythat the inference is valid. Every scientist aims to arrive at correct conclusionson the basis of certain evidence. He has to see that his reasoning is inaccordance with valid argument patterns. Such knowledge is provided by logic.Logic provides us the tools for the analysis of arguments. Knowledge of logic ishelpful for the formation of critical habit of mind and for detecting fallacies inthinking.

21

By practicing various logical exercises our intellect become sharpened. Logiccultivates and develops our reasoning power. It trains and disciplines the mind. Intellectual discipline is of great importance to man.

Deriving valid conclusions from the premises: Examples

1.All systematic knowledge of a particular subject is Science

Logic is a systematic knowledge of a particular subject

.`. ……………………………………….

Answer- Logic is a Science

2All logicians are those who know how to reason well

Some not-good reasoners are logicians

.`. ……………………………………….

Answer-Some not-good reasoners are those who know how to reason well

3.All repeaters are women students

All who have passed are repeaters

.`. ……………………………………….

Answer-All who have passed are women students

4. ,All youths are inexperienced

All students are youths



.`. ……………………………………….

Answer-All students are inexperienced

5. No lazy men are great

Gopal is lazy

22

.`. ……………………………………….

Answer- Gopal is not lazy

6. All successful students are clever

Some mischievous students are successful

.`. ……………………………………….

Answer—Some mischievous students are clever

7. No tale –bearers are reliable

Some men are tale-bearers

.`. ……………………………………….

Answer—Some men are not reliable.

8. All misers are unhappy

X is a miser

.`. ……………………………………….

Answer— X is unhappy

9. All men are mortal

X is a man

.`. ……………………………………….

Answer—X is mortal

10. All wicked people are unhappy

Some people are wicked

.`. ……………………………………….

Answer—Some people are unhappy

11. All statesmen are far-sighted



23

All politicians are statesmen

.`. ……………………………………….

Answer –All politicians are far-sighted

12. All statesmen are far-sighted

Some politicians are not far-sighted

.`. ………………………………………

Answer—Some politicians are not statesmen

13. All clever people are enterprising

All publishers are clever

.`. ………………………………………

Answer—All publishers are enterprising

14. No men are angels

Some rational beings are men

.`. ………………………………………

Answer—Some rational beings are not angels

15. All greedy men are discontented

All misers are greedy

.`. ………………………………………

Answer—All misers are discontented

16. All discontented persons are unhappy

All misers are discontented

.`. ………………………………………

24

Answer— All misers are unhappy

17. All unhappy men are selfish

All misers are unhappy

.`. ………………………………………



Answer—All misers are selfish

18. No mortals are perfect

All men are mortal

.`. ………………………………………

Answer —No men are perfect

19. No men are perfect

All politicians are men

.`. ………………………………………

Answer---No politicians are perfect

20. No politicians are perfect

All ministers are politicians

.`. ………………………………………

Answer —No ministers are perfect

21. All men are mortal

Socrates is a man

.`. ………………………………………

Answer —Socrates is mortal

22. All organisms are mortal

All men are organisms

25

.`. ………………………………………

Answer —All men are mortal

23.All composite things are mortal

All organisms are composite

.`. ………………………………………

Answer —All organisms are mortal

%%%%%%

applicationsof logical reasoning - university of … philosophy - vi sem. additional... ·...

Documents