SYLLOGISM
Syllogism is a part of analytical reasoning in which we
have two or more propositions, often referred to as TYPES OF STATEMENTS
statements that show the relation between two or
more elements. We need to derive that relation in the There are two types of statements: Positive and
form of conclusions. Negative. These are further divided into four types of
In order to derive the relation of elements, we draw a propositions: A, E, I, and O.
Venn Diagram based on the given statements and Meaning of A, E, I, and O are:
deduce certain relations among elements in the form
of conclusions.
Sr. No. Types of Statement Represented by
You can understand this interrelation with the help of
the letter
the diagram given below:
1 Universal A (All)
STATEMENT 2 Universal E (No)
3 Particular I (Some)
4 Particular O (Some Not)
VENN
DIAGRAM
CONCLUSION
Statement Venn Diagram Conclusion Format with examples (using all, some, some not, no)
It gives us It gives us It tells about
information information about the hidden
about the the relation relation
relation between different between
between elements. It is elements that is
different illogical in nature. depicted in the
elements. It is statement.
illogical in
nature. Secondary keywords used at the place of Some, All, Some
Not, and No which you will see in statements.
So, basically, syllogism contains two or more
propositions, on the basis of which, we can derive an
inference or conclusion.
Statement 1: Some A are B
Conclusions that follow for this statement
• Some A are not B is a possibility.
• All A are B is a possibility.
• Some B are A
• Some B are not A is a possibility
• All B are A is a possibility
(* - This is based on one condition. The condition for Statement 2: All A are B
‘Only’ is explained in the below mentioned topics).
We have two methods to derive the hidden relations
between elements.
Conclusion that follows for this statement
• Some A are B.
EULER’S CIRCLE REPRESENTATION • Some B are A.
• Some B are not A is a possibility
• All B are A is a possibility
Pictorial representation of prepositions is done by Euler’s
circles (Venn diagram) as follows:
3 GOLDEN RULES (POSSIBILITY CASE)
Rule 1: Whenever there is no relation between any two
elements according to the Venn Diagram, then all types
of definite conclusions will be treated wrong (can’t say)
whereas all types of possible conclusions between the
same will be true.
Example: Some A are B.
Some B are C.
Least possible Venn Diagram:
Conclusions:
1. Some A are C - False (since there is no direct relation
DERIVING CONCLUSIONS shown between A and C)
2. Some A are not C - True
Conclusion can be of two types: Definite conclusion Rule 2: Whenever we will be required to draw a true
and Possible Conclusion conclusion regarding the Blank Space (space about
A definite conclusion is the one that is definitely true as
which we have no definite information) of any Venn
derived from the statement whereas a possible
Diagram, we will have to use the word possibility
conclusion is the one that is not necessarily true but it otherwise the conclusion will be treated as false.
can be a possibility. Example: All A are B.
Least possible Venn Diagram:
INFORMATION ABOUT “EITHER – OR”
I. The conclusion must be definitely false but their
Conclusions: possibility must be true.
1.Some B are A - True II. One Conclusion must be positive and another must be
2.All B are A - False negative so, that it forms a complementary pair.
3.All B are A is a possibility - True III. There are only three complementary pairs: ‘Some +
Rule 3: Already existing relation between elements or No’, Some + Some not’, and ‘All + Some not’ IV. Subject
already restricting relation between elements never and Object must be the same in both the conclusions for
allow possibility. the ‘All + Some not’ case.
Example: All A are B.
Least possible Venn Diagram:
SYLLOGISM – TRICKS AND RULES
1. With two particular statements, no universal
Conclusions:
conclusion is possible.
1. Some A are B is a possibility - False
2. With two positive statements, no negative conclusion
2. Some B are A is a possibility - False
is possible.
3. All A are B is a possibility - False
3. With two negative statements, no positive conclusion
4. All B are A is a possibility – True
is possible.
4. The common term/middle term should be distributed
THE CASE OF ‘ONLY’ at least once and the common term should not appear in
the conclusion.
5. If one proposition/premise is negative then the
‘Only’ is used as a secondary keyword for ‘All’. But there conclusion is negative.
are certain things that you must understand in order to 6. If one premise is particular then the conclusion is
avoid any kind of confusion or mistake in the exam. particular.
Suppose the given statement is: Only B is A 7. With two particular statements, no conclusion is
This means that A can fall only under B (or we can say possible, exactly when an ‘I’ type of statement is given
All A are B), but this does not necessarily mean that ‘All and then by reversing it an ‘I’ type of conclusion is
B are A’. possible.
Example: 8. “All A are not B” is the same as “Some A are not B”.
Statement: Only Axe is cut. Some 9. “Only A are B” is the same as “All B are A”.
Axe is hand. 10. “No A is B” is the same as “No A are B”.
Least possible Venn Diagram: 11. Any “All” and “All” sentence will always imply an “All”
conclusion.
12. Any “All’ and “No” sentence will always imply a “No”
conclusion.
13. Any ‘All” and “Some” sentence will always imply a
Here, we can conclude: ‘All Cut are Axe’, ‘Some Axe are
“No” conclusion.
Cut’. But we cannot conclude: ‘All Axe are Cut’, ‘Some Cut
14. Any “Some” and “All” sentence will always imply a
are Hand’. It is given that ‘Only Axe are Cut’. This means
“Some” conclusion.
that ‘Cut’ will fall only under ‘Axe’ and no other element.
15. Any “Some” and “No” sentence will always imply a
“Some not’ conclusion.
16. Any “Some” and “Some” sentence will always imply a
“No”
conclusion.
NOTE: If a term is not distributed in the premises then it
cannot be distributed in the conclusions. Let us
understand syllogism through some examples.
Conclusion I: Some mouses are scanners. - True (As it is
given that some scanners are mouses)
Direction (Q:1 - Q:4) In the following question some
Conclusion II: No keyboard is a printer - False (It is
statements are followed by some conclusions. You have
possible but not definite.)
to take the given statements to be true even if they seem
Conclusion III: No keyboard is a mouse - False (Some
to be at variance from commonly known facts. Read all
mouses are keyboards so, no keyboard is a mouse is
the statements and decide which of the given
definitely false.)
conclusion/conclusions logically follows from the given
statements
Q:3 Statements: Only dog is cat. No dog is lion. Some cat
is not rat.
Q:1 Statement: All windows are rooms. No room is gate.
Conclusions:
Conclusion: I. No window is gate
I. Some dog is lion
II. Some windows can be gate
II. Some cats can be lion
1. Only I is true 2. Only II is true
III. All rats are lion
3. Neither I nor II is true 4. Either I or II is true
1. Only I is true 2. Only II is true
Solution: (1) Only I is true
3. Neither I nor II is true 4. None follows
The least possible Venn Diagram for the given statements
Solution: (4) None follows
is drawn below:
The least possible diagram for the given statements is:
Conclusion: I. No window is gate: True (We have given all
windows are rooms and no room is gate so no window is
gate is true as all window is a part of room and there is
negative relation between room and gate.) Conclusions: I. Some dog is lion. - False (As No dog is lion,
II. Some windows can be gate: False (As all window is a so some dog is lion is false.)
part of room and there is negative relation between II. Some cat can be lion. - False (Only dog is cat and no
room and gate so ‘No window is gate’.) dog is lion so, some cat can be lion is false.)
III. All rat is lion. - False (It is not definite)
Q:2 Statements: No printer is a scanner. Some scanners
are mouses. Some mouses are keyboards. Q:4 Statements: Only a few Jitendra is Subodh. No
Conclusions: I. Some mouses are scanners. Subodh is Anju.
II. No keyboard is a printer. Conclusions:
III. No keyboard is a mouse. I. Some Anju being Jitendra is a possibility.
1. Only I is true 2. Only II is true II. Some Anju can be Subodh.
3. Neither I nor II is true 4. Either I or II is true 1. Only I is true 2. Only II is true
Solution:(1) Only conclusion I follows 3. Neither I nor II is true 4. Either I or II is true
By making the least possible Venn diagram we get: Solution:(1) Only conclusion I follows
By making the least possible Venn diagram we get
Conclusions:
I. Some Anju being Jitendra is a possibility: True (It is
possible as there is no negative relation between the
elements)
II. Some Anju can be Subodh: False (As no Subodh is
Anju) Hence, the correct answer is Only conclusion I
follows.
