9syllogism

CHAPTER 9

SYLLOGISM

Reasoning

Presented By : Saurabh Trivedi

These questions are totally based upon the logic. If we solve these questions with the help of Venn diagrams then we can get the conclusions easily.

Remember that these Venn diagrams are just a medium to solve such questions.

A question can have lots of diagrams which means we can draw several figures by a statement but we have to draw the easiest figure first because it will enable us to solve the question in minimum time. Like we have many routes to go home but we always take the shortest possible route.

About Syllogism

Types of sentences

• (i) All Apples are Papayas• (ii) Some Apples are Papayas+ve• (iii) No Apple is Papaya• (iv) Some Apples are not Papayas-ve

(I) All apples are papayas

Apples

papayas

Diagrammatical Representation

(II) Some Apples are papayas


Apples papayas

(III) No Apple is papaya

This line shows the negative relation between subject (Apple) & predicate (papaya) which means any part of Apple can not be Papaya.


Apple papaya

(iv) Some Apples are not papayas

In the above figure shaded portion shows that those apples are not papaya.

Apple papayas


We can also describe the above statements through some more diagrams.

i.e.-

Like - All Apples are Papayas & Apples = Papayas

Where A = B its possible figure

Apples

papayas

Apples

papayas

Alternative Representations

Some Apples are Papayas

The possible figure are given below.

(I) (II)

(III) (IV) A = B


Apples papayas

Apple

papayas

Applepapayas

Applepapayas

No A are B –


(I)

(II)


Apple papaya

Apple papaya

AppleApples

Some A Apples are not Papayas –


(I) (II)

(III) (IV)


Apples papayaspapayas

Apples

Apples

papayas

Apples

AppleApples papayas

The trend shows that basically there are two kinds of conclusions. One requires definite case as a conclusion and another requires case of possibility.

Definite Case-

(1) If only conclusion I follows.

(2) If only conclusion II follows.

(3) If either conclusion I or II follows.

(4) If neither conclusion I nor II follows.

(5) If both conclusion I and II are follow.

How to Conclude ???

Q.1. Statement : All gems are pens

All pens are balls

Conclusions : I. All gems are balls.

II. Some gems are balls.

Examples

Gems

Pens

Balls

Both conclusions follow

Q.2. Statement : Some Bats are Goats.

All Goats are Hats.

No Hat is Tap.

Conclusions : I. Some Bats are Hat.II. No Goat is Tap

Examples

Bat Goat Hat Tap

Both conclusions follow

Q.3. Statement : Some Mats are Boats.Some Boats are Grains.

All Grains are pebbles.No pebble are tap.

Conclusions : I. Some Mats are Grains.

II. No pebbles are tap.

Examples

Boat Grains Pebbles TapMat

Only Conclusion II follow

Q.4. Statement : All Goat are Hat

Some Hat are Bat

No Bat are Tap

Conclusions : I. Some Tap are Goat

II. No Tap are Goat

Examples

BatGoatHat

Tap

Only Either I or II follow

Explanation

BatGoatHat

Tap

BatGoatHat

TapBatGoat

Hat

Tap

Some Tap are Goat No Tap is Goat

Case of possibilities.

In most of the questions the case of possibility is applicable whenever we find the given conclusion as neither definitely true nor definitely false. That conclusion may be possibly true for given statements.

How to Conclude ???

Statement : All A are B

Conclusions : I. Some A are B

II. No A are B

III. All B are A

How to Conclude ???

A

B

How to Conclude ???

A

B

AA B A

B

A B

Statement : Some A are B

Conclusions : I. Some B are A being a possibility.

II. No A are B being a possibility.

III. All B are A being a possibility.

How to Conclude ???

A B A BAA B

Q.5. Statement : Some A are B.

No B are C.

All C are D.

Conclusions : I. Some A being D is a possibility.

II. All A being D is a possibility.

Examples

A B DC

Examples

II. All A being D is a possibility.

A

B

C

I. Some A being D is a possibility.

B

C

A B DC

A

D D

Ø Require same subject and predicate in two different conclusion

Ø Relation must not be clear (according to statement) between subject & predicate.

Ø One conclusion must be positive and another must be negative.

Ø Either condition will not be allowed between ‘All’ type ‘No’ type sentence.

Ø Either conclusions can easily be identified if we focus specially upon those objects which are same.

Ø Keep this thing in mind that if the relation between 2 objects is not clear then we can not come to any conclusion and in case the relation between 2 objects is clear then we can directly come to the conclusion without any problem.

Ø Either case can be applied only in indirect relations where the relations between subject and predicate is not determined.

For Complementary Conclusions…

Questions Based on Previous Exams

Q.31-35.In each of the questions below, two/three statements are given followed by conclusions/group of conclusions numbered I and II. You have to assume all the statements to be true even if they seem to be at variance from the commonly known facts and then decide which of the given two conclusions logically follows from : the information given in the statements.

Give answer (1) if only conclusion I follows

Give answer (2) if only conclusion II follows

Give answer (3) if either conclusion I or II follows

Give answer (4) if neither conclusion I nor II follows

Give answer (5) if both conclusions I and II follow

SBI 28/04/2013

Q.31-32.Statements : Some squares are circles.

No circles is a triangle.

No line is a squares.

Q.31. Conclusions : I. No triangle is a squares.

II. No line is a circles.

Q.32. Conclusions : I. All squares can never be triangle.

II. Some line are circles.

SBI 28/04/2013

Q.33-34.Statements : All songs are poems.

All poems are rhymes.

No rhymes is a paragraph.

Q.33. Conclusions : I. All rhymes are poems.

II. All songs are rhymes.

Q.34. Conclusions : I. No songs is a paragraph.

II. No poems is a paragraph.

SBI 28/04/2013

Q.35. Statements : Some dews are drops.

All drops are stones.

Conclusions : I. At least some dews are stones.

II. At least some stones are drops.

SBI 28/04/2013

Q.12-18.In each group of question below are two/three statements followed by two conclusion numbered I and II. You have to take the given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the two/three statements disregarding commonly known facts.

Give answer (1) If only I follows.

Give answer (2) If only II follows.

Give answer (3) If either I or II follows.

Give answer (4) If neither I nor II follows.

Give answer (5) If both I and II follows.

CWE PO 17/06/2012

Q.12. Statements : Some exams are tests.

No exam is a question

Conclusions : I. No question is a test.

II. Some tests are definitely not exams.

CWE PO 17/06/2012

Q.13-14.Statements : All forces are energies.

All energies are powers.

No Power is heat.

Q.13. Conclusions : I. Some forces are definitely not powers.

II. No heat is force.

Q.14. Conclusions : I. No energy is heat.

II. Some forces being heat is a possibility.

CWE PO 17/06/2012

Q.15-16.Statements : No note is a coin.

Some coins are metals.

All plastics are notes.

Q.15. Conclusions : I. No coin is plastic.

II. All plastics being metals is a possibility.

Q.16. Conclusions : I. No metal is plastic.

II. All notes are plastics.

CWE PO 17/06/2012

Q.17. Statements : Some symbols are figure.

All symbols are graphics.

No graphic is a picture.

Conclusions : I. Some graphics are figures.

II. No symbol is a picture.

CWE PO 17/06/2012

Q.18. Statements : All vacancies are jobs.

Some jobs are occupations.

Conclusions : I. All vacancies are occupations.

II. All occupations being vacancies is possibility.

CWE PO 17/06/2012

Q.6-10.In each question below are two/three statements followed by two conclusions numbered I and II. You have to take the two/three given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the given statements disregarding commonly known facts. CWE PO 18&09&2011

Give answer (1) if only I follows

Give answer (2) if only II follows.

Give answer (3) if either I or II follows.

Give answer (4) if neither I nor II follows.

Give answer (5) if both I and II follow.

CWE PO 18/09/2011

Q.6-7. Statements: All gliders are parachutes.

No parachute is an airplane.

All airplanes are helicopters.

Q.6. Conclusions: I. No glider is an airplane.

II. All gliders being helicopters is a possibility.

Q.7. Conclusions: I. No helicopter is a glider.

II. All parachutes being helicopters is a

possibility.

CWE PO 18/09/2011

Q.8. Statements : Some mails are chats.

All updates are chats.

Conclusions : I. All mails being updates is a possibility.

II. No update is a mail.

CWE PO 18/09/2011

Q.9 - 10. Statements: No stone is a metal.

Some metals are papers.

All papers are glass.

Q.9. Conclusions : I. All stones being glass is a possibility.

II. No stone is a paper.

Q.10. Conclusions : I. No glass is a metal.

II. At least some glass is metal.

CWE PO 18/09/2011

Q.47-53.In each question below are three statements followed by two conclusions numbered I and II. You have to take the three given statements to be true even if they seem to be at variance from commonly known facts and then decide which of the given conclusions logically follows from the three statements disregarding commonly known facts. BOB 13-03-2011

Give answer (1) if only I follows.

Give answer (2) if only II follows.

Give answer (3) if either I or II follows.

Give answer (4) if neither I nor II follows.

Give answer (5) if both I and II follow.

BOB 13/03/2011

Q.47-48.Statements : Some stars are moons.

All moons are planets.

No planet is universe.

Q.47 Conclusions : I. All moons being stars is a possibility.

II. No universe is star.

Q.48. Conclusions : I. At least some planets are stars.

II. No moon is universe.

BOB 13/03/2011

Q.49-50.Statements : All sticks are plants.

All plants are insects.

All insects are amphibians.

Q.49. Conclusions : I. At least some amphibians are plants.

II. All sticks are insects.

Q.50. Conclusions : I. All amphibians are sticks.

II. All plants are amphibians.

BOB 13/03/2011

Q.51-53.Statements : All apartments are huts.

No hut is a building.

All buildings are cottages.

Q.51. Conclusions : I. No cottage is an apartment.

II. Some cottages are apartments.

Q.52. Conclusions : I. No apartment is a cottage.

II. Some buildings being apartments is a possibility.

Q.53. Conclusions : I. Some cottages being apartments is a possibility.

II. No cottage is a hut.

BOB 13/03/2011

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9syllogism