SYLLOGISMS
Syllogisms is one of the main topics in Verbal or Logical
Reasoning in various competitive exams like SBI PO, IBPS PO, SBI Clerk, IBPS
Clerk, SBI Associate PO, CAT, IBPS RRB, SSC CGL, NICL AO, NIACL AO, LIC AAO,
etc. Generally 5-6 questions are asked on this topic alone in each of these
exams. As it is an important, easy and scoring topic, you should have good
command over it. Follow some basic concepts and rules explained in this first
article of the series, and you can easily solve these types of questions in
just a few seconds.
What are Syllogisms
A syllogism is a kind of logical argument that applies
deductive reasoning to arrive at a conclusion based on two or more premises
(also called propositions) that are asserted or assumed to be true.
The conclusion asserts no more than what is already
contained, implicitly, in the premises. If it does, the syllogism is invalid.
An important thing to be kept in mind is that one has to
take the given statements to be true even if they seem to be at variance from
commonly known facts.
Types of Premises
A premise is a statement which comprises of two terms; a
subject and a predicate, connected by a relation.
·
Subject is that about which something is said
and
Predicate states something about the subject.
If another premise contains one of these terms (known as the
common term), we can deduce a relation between the non-common terms.
Now we are going to
look in to concept :-
Please kip pen with you go through
each concept one by one and understand how to draw venn diagram for each
concept.
I insist you to go one by one. Understand the one concept and then go to next one.
SELECTIONS
There are
four categories you must remember. These tell you how many objects have a
certain attribute or how many you have selected.
1. All (i.e.
you can select every object in the group.)
2. Some (i.e.
you can select a few objects in the group.)
3. None (i.e.
you can leave out all objects in the group.)
4. Some Not
(i.e. you can leave out a few objects in the group.)
CONCEPTS :-
The general representation
of this premise is as shown below :
But there may be a case
where A=B, then also this premise is true.
Concept 2 - No A are B
This premise is represented
as:
Concept 3 - Some A are B
It can be depicted as:
The space between A & B denotes the premise.
NOTE: Looking at this general representation, one may perceive that
if ‘some A are B’ then ‘some A are not B’.
But the following cases can also imply ‘Some A are B’
- All B are A.
- All A are B.
- A and B are identical.
We can see that in the case where
(i) A is a subset of B or
(ii) A=B,
the premise ‘some A are not B’ does not hold true.
Concept 3 - Some A are not B
This premise can also be
represented as
Solving Syllogisms using Venn diagram
Venn diagram method
is an effective and precise method to solve syllogism problems.
You can follow the
below steps to answer them:
In order to solve a
syllogism,
1. draw the standard diagram based on the given statements.
2. Then try to check
which of the given conclusions follow in every possible case.
3. If a conclusion is
true for one case but is negated for the other possible representation, it is
not considered as a conclusion.
4. In other words, a
conclusion follows only if it is true for all the possible cases.
EXAMPLE:-
EXAMPLE-1
All A are B. Some B
are C.
Conclusion: All A
being C is a possibility.
Conclusion is true.
Possibility figure
–
EXAMPLE-2
No stone is a
white. Some white are papers.
Conclusions: I. All
stones being paper is a possibility.
Possibility figure –
Conclusion is true.
EXAMPLE-3
Some mouse is cat.
All mouse are
pets. No pet is animal.
Conclusions: I. All
mouse being animal is a possibility.
Conclusion is false
because possibility figure is not possible.
If we say all mouse
being animal is possibility is true, than given statements No pet is animal
will be wrong. Here in the statement it is given No pet is animal and All mouse
is pet. So we can make also conclusion here that no mouse are animal is true.
Important Rule:
Restatement is not a conclusion – Conclusion has to be different from
the statement.
E.g. Statement – All A are B
Conclusion – All are B. (invalid) Conclusion does not follow.
Conclusion – Some A are B (follow) Conclusion follows.
Note: If statement and conclusion is same then, conclusion does not follow.
This rules also follows in possibilities case
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