9syllogism
DESCRIPTION
This presentation is aimed to help aspirants and faculty members for preparation of various competitive exams.TRANSCRIPT
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
Diagrammatical Representation
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.
Diagrammatical Representation
Apple papaya
(iv) Some Apples are not papayas
In the above figure shaded portion shows that those apples are not papaya.
Apple papayas
Diagrammatical Representation
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
Alternative Representations
Apples papayas
Apple
papayas
Applepapayas
Applepapayas
No A are B –
The possible figure are given below.
(I)
(II)
Alternative Representations
Apple papaya
Apple papaya
AppleApples
Some A Apples are not Papayas –
The possible figure are given below.
(I) (II)
(III) (IV)
Alternative Representations
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