8. Syllogisms
Introduction:-
Syllogism is an important topic of logical reasoning. Generally a set of 5-6 questions asked in the competitive examination this type of question can be solved using Venn-diagram. Generally there are following type of syllogism.
Statement Type
Syllogism is an important topic of logical reasoning. Generally a set of 5-6 questions asked in the competitive examination this type of question can be solved using Venn-diagram. Generally there are following type of syllogism.
Statement Type
| Type 1 | All books are pen |
| Type 2 | No book is pen |
| Type 3 | Some book are pen |
| Type 4 | Some book are not pen |
Conclusion type
Type 1: All books are pen
Type 2: No books are pen
Type 3: Some books are pen
Type 4: some books are not pen
Type 5: All books are pen possibly
Type 6: At least some books are pen
In this type of question some statement are given and you have to find out conclusion from its. Let’s take a statement
'All books are pen'
Now 'it is written that all books are pen what conclusion you make. You make following conclusion on it
(a) Some pens are book
(b) Some books are pen
Now see Venn-diagram of it
Making Venn diagram
All books are pen
Conclusion:
Some pens are book
Some books are pen
Conclusion:
Some pens are book
Some books are not pen
Conclusion:
Not conclusion
Now boldly statement of syllogism is divided in three part
- Positive
- Negative
- Possibly
Positive part
All and some
Example: All books are pen. All pens are copy.
In this type of question you have to prove statement wrong. If you not prove it this means that this is true.
Suppose from above diagram we have to find out 'No book are copy1 but we can prove it wrong. So it statement is not followed.
Negative part
No book is pen
In negative part we have to prove the statement right if we cannot prove it this means this statement is followed or true.
Statement: All books are pen. No pen is copy.
Conclusion: No book is copy.
For using above two statements we cannot prove above conclusion right. So it follows.
Possibly part
In this type of part we have to make all possibility and if one of the things say that it is possible then our conclusion become true otherwise wrong.
Statement: All books are pen.
Conclusion: All pens are book possibly Or, It is possible all pen are book.
Now there will be two possibilities. One is that both book and pen are overlap. When both are overlapping then our conclusion will be right, it will follow.
At least statement
This statement is same as some statement
Complementary pair
Some time pair of statement came like
(a) no boy are student and
(b) some boy are student
See carefully these are only two case and one of the must follow so generally when these type of question came we can mark one of them right. Some not statement
"Some not' is opposite to "All" type statement if "All" being true then some not being false, and vice versa.
Statement: Some A are B.
No B are C.
Conclusions: I. Some A are not C.
II. Some C’s are not A.
1st Conclusion is Some A are not C. for finding it we have to find out is it possible that All A re C if it is possible then conclusion is false otherwise true.
Now Venn diagram is
We cannot prove that All A are C because some part of A which is b, is never be C.
Alternative Diagram 2 Now from II: We have to prove that All C are A from following diagram-
So it cannot be follow.
So in short if it given some A re not B you try to prove it that All A are B. If you can prove it then some "A are not B" will not follow and vice versa.
EXERCISE
Directions 1 -5
(a) If only conclusion I follows.
(b) If only conclusion II follows.
(c) If either conclusion I or II follows.
(d) If neither conclusion I nor II follows.
(e) If both conclusions I and II follow.
- Statements:
All cots are tables.
All tables are trains.
All trains are buses.
Conclusions:
I. All tables are buses.
II. All trains are tables.
- Statements:
Some mobile are computers.
Some computers are calculators.
Some calculators are phones.
Conclusions:
I. Some phones are computers.
II. Some computers are mobile.
- Statements:
All spoons are bowls.
Some bowls are glasses.
Some glasses are plates.
Conclusions:
I. Some glasses are spoons.
II. Some plates are bowls.
- Statements:
Some envelopes are packets.
Some packets are boxes.
All boxes are parcels.
Conclusions:
I. Some parcels are packets.
II. Some parcels are boxes.
- Statements:
Some desks are tents.
Some tents are rivers.
All rivers are ponds.
Conclusions:
I. Some ponds are tents.
II. Some ponds are desks.
Directions for 6-10:- - Statements:
Some cards are plastics.
Some plastics are metals.
All metals are pots.
Conclusions:
I. Some pots are cards.
II. No pot is a card.
- Statements:
All goats are flowers.
No flower is branch.
Some branches are roots.
Conclusions:
I. Some roots are goats.
II. No root is goat.
- Statements:
All stars are suns.
Some suns are planets.
All planets are satellites.
Conclusions:
I. Some satellite are stars.
II. No star is a satellite
- Statements:
Some sweets are salt.
No salt in spice.
Conclusions:
I. No spice is sweet.
II. No spice is salt.
- Statements:
All leaves are flowers.
No flower is branch.
Some branches are fruits.
Conclusions:
I. Some fruits are leaves.
II. No fruit is leaf.
Directions for 11-15:-
(a) If only conclusion I follows.
(b) If only conclusion II follows.
(c) If either conclusion I or II follows.
(d) If neither conclusion I nor II follows.
(e) If both conclusions I and II follow.
- Statement:
Some water are tea.
No tea are coffee.
Conclusions:
I. Some water are tea.
II. No water is coffee.
- Statement:
Some dog are cow.
No cow is cat.
Conclusions:
I. No dog is cat
II. No cat is dog
- Statement:
Some pen are clips.
Some clips are pin.
Conclusions:
I. Some pins are pens
II. No pin is a pen
- Statements:
All book are cities
All states are cities
some cities are countries.
Conclusions:
I. Some state are book
II. some countries are states
- Statement:
All book are pen
No book is a copy
Conclusions:
I. No pen is a copy
II. At least some book is copy.
Directions 16-20:-
(a) If only conclusion I follows.
(b) If only conclusion II follows.
(c) If either conclusion I or II follows.
(d) If neither conclusion I nor II follows.
(e) If both conclusions I and II follow
- Statements:
Some stones are rocks.
All rocks are boulders.
Some boulders are mountains.
All hills are mountains.
Conclusions:
1. Some stones are mountains.
II. Some hills are boulders.
III. Some boulders are stones.
IV. All mountains are hills.
(a) None follows
(b) Only If follows
(c) Only II and III follow
(d) Only III follows
(e) None of these
- Statements:
All arrows are bows.
All bows are swords.
Some swords are daggers.
All daggers are knives.
Conclusions:
I. All knives are bows.
II. Some swords are knives.
III. All bows are arrows.
IV. All arrows are swords.
(a) Only II follows
(b) Only II and IV follow
(c) Only III and IV follow
(d) Only I and III follow
(e) None of these
- Statements:
Some pianos are violins.
Some violins are drums.
All drums are guitars.
No guitar is a flute.
Conclusions:
I. Some guitar are pianos.
II. Some drums are flutes.
III. Some pianos are drums.
IV. No flute is a drum.
(a) None follows
(b) Only I follow
(c) Only either II or IV follows
(d) Only IV follows
(e) None of these
- Statements:
Some cycles are bikes.
No bike is flower.
All flowers are goats.
Conclusions:
I. No goat is cycle.
II. Some flowers are cycles.
III. Some goats are bikes.
(a) None follows
(b) Only I follow
(c) Only II follows
(d) Only III follows
(e) Only II and III follow
- Statements:
Some shoes are socks.
All socks are towels.
All towels are bed sheets
No bed sheet is blanket.
Conclusions:
I. No towel is blanket.
II. Some shoes are towels.
III. Some shoes are bed sheets.
(a) Only I and II follow
(b) Only II and III follow
(c) Only I and III follow
(d) All follow
(e) None of these
Directions 21-25:- - Statements:
All chairs are tables.
All tables are telephones.
All telephones are cell phones.
No cell phone is computer.
Conclusions:
I. All cell phones are tables.
II. Some chairs are computers.
III. No chair is computer.
(a) Only I follow
(b) Only II follows
(c) Only III follows
(d) Only either II or III follows
(e) None of these
- Statements:
Some rocks are hills.
All hills are mountains.
All mountains are rivers.
No river is Canal.
Conclusions:
I. All rocks are rivers.
II. Some hills are canals.
III. Some rivers are canals.
(a) Only I follow
(b) Only II and III follow
(c) Only I and III follow
(d) Only II follows
(e) None follows
- Statements:
All rats are cats.
No cow is cat.
All dogs are cows.
Conclusions:
I. No dog is rat.
II. No dog is cat.
III. No cow is rat.
(a) None follows
(b) Only III follows
(c) Only I and II follow
(d) Only II and III follow
(e) All follow
- Statements:
Some walls are doors.
Some doors are cots.
Some cots are chairs.
Conclusions:
I. Some chairs are doors.
II. Some cots are walls.
III. No chair is door.
(a) Only II follows
(b) Only III follows
(c) Only either I or III follows
(d) Only I follow
(e) None of these
- Statements:
All books are leaves.
Some leaves are jungles.
No jungle is box.
Conclusions:
I. Some jungles are books.
II. No book is box.
III. Some leaves are boxes.
(a) None follows
(b) Only I follow
(c) Only II follows
(d) Only III follows
(e) Only I and II follow
Direction for 26-30:- - Statements:
All green are vegetables
All bears are green
Some green are nuts
Conclusions:-
I. All nuts are vegetables is a possibility
II. Some bears are nuts is a possibility
- tatements:
No books is shoe
Some shoes are stocks
No stocks is shirt
Conclusions:-
I. Some books are shirts is a possibility
II. Some shirts are shoes is a possibility
- Statements:
All books are shops
Some houses are shops
Some houses are miracles
Conclusions:-
I. Some miracles are shops is a possibility
II. Some banks are houses is a possibility
- Statements:
Some cups are not bolts
All dusters are balls
All cups are balls
Conclusions:-
I. All bolts are cups
II. Some dusters are cups is a possibility
- Statements:
All horses are cows
Some cows are sheep
All oxen are horses
Conclusions:-
I. Some oxen are sheep
II. All sheep being horses is a possibility
Directions for 31-35:-
- Statements:
Some clothes are fabrics.
No accessories is a dress
All dresses are fabrics
Conclusions:-
I. Some clothes are dresses is a possibility
II. All clothes are accessories is a possibility
III. Some fabrics are not accessories is a possibility
IV. All fabrics are accessories is a possibility
(1) only I & II follows
(2) Only II & III follows
(3) Only II follows
(4) Only I, II, III follows
(5) Only I, III & IV follow
- Statements:
All kings are queens
All kings are diamonds
All aces are diamonds
Conclusions:-
I. All diamonds are queens is a possibility
II. Some diamonds are not kings is a possibility
III. All aces are queens is a possibility
IV. All queens are diamonds is a possibility
(1) Only I, II & III follow
(2) Only II & III follow
(3) Only II, III & IV follow
(4) All follow
(5) Only I, III & IV follow
- Statements:
All dogs are cats
No cats are rats
No goat is dog
Conclusions:-
I. Some cats are not goats is possibility
II. Some cats are goats is a possibility
III. No dog is rat is a possibility
IV. Some rats are dogs is a possibility
(1) Only II & III follow
(2) Only I, II & III follow
(3) Only III & IV follow
(4) Only I, II & IV follow
(5) All follow
- Statements:
Some notes are not records
No records is a warning
All warning are instructions
Some instructions are not hints
Conclusions:-
I. No records is a hint is not a possibility
II. No instruction is a warning is a possibility
III. Some hints are warning is a possibility
IV. All notes are hints is a possibility
(1) Only I & II follow
(2) Only I, II & III follow
(3) Only III & IV follow
(4) All follow
(5) None follow
- Statements:
No switch is a plug
No pug is equipment
No Equipment is a board
Conclusions:-
I. All boards are switches is a possibility
II. Some boards are plugs is not possibility
III. Some switches are plugs is a possibility
IV. Some equipment are switches is a possibility
(1) Only I & IV possibility
(2) Only II & III possibility
(3) Only I, III & IV possibility
(4) Only I, II & III possibility
(5) All follows
Directions 36-40:- - Statements:
Some herbs are not plants
All herbs are shrubs
Conclusions:-
I. All Shrubs are plants is not a possibility
II. All plants are shrubs is not a possibility
- Statements:
Some knights are Bishops
Some bishops are not pawns
All rocks are pawns
Conclusions:-
I. Some pawns are rocks
II. Some rocks are not bishops is not a possibility
- Statements:
Some mobiles are not Desktops
All desktops are computers
Some computers are not laptops
Conclusions:-
I. Some desktops are not laptops is not possibility
II. Some computers are mobiles
- Statements:
All banks are shops
Some houses are shops
Some houses are miracles
Conclusions:-
I. Some miracles are not shops is not a possibility
II. Some Banks are houses is a possibility
- Statements:
Some cups are not bolts
All dusters are balls
All cups are balls
Conclusions:-
I. All bolts are not balls is not a possibility
II. All dusters are bolts is a possibility
(1) If only conclusion I follow
(2) If only conclusion II follow
(3) If either Conclusion I (or) II follow
(4) if neither Conclusion I (nor) II follow
(5) If both I & II follows
| ANSWERS | |||||||
| 1 | A | 11 | a | 21 | c | 31 | d |
| 2 | b | 12 | d | 22 | e | 32 | d |
| 3 | d | 13 | c | 23 | e | 33 | b |
| 4 | e | 14 | d | 24 | c | 34 | c |
| 5 | a | 15 | d | 25 | a | 35 | a |
| 6 | c | 16 | d | 26 | e | 36 | a |
| 7 | c | 17 | b | 27 | e | 37 | a |
| 8 | c | 18 | d | 28 | e | 38 | d |
| 9 | b | 19 | a | 29 | b | 39 | b |
| 10 | c | 20 | d | 30 | b | 40 | b |
Prepared by,
IACE, Hyderabad
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