Friday, 17 July 2015

Solving Syllogism using Venn diagram

Syllogism for bank exams

Solving syllogism is always confusing .No more confusion here onwards. Conventional methods are usually time consuming .It is okey if the problem is 2 statement syllogism. But it is not the case if the problem is 3,4 or 5 statement syllogism .Conventional method will eat your valuable time during exams. Please try to follow Venn diagram method explained below.
Before solving questions ,let us draw Venn diagram for possible statements.

1.Statement:”All A are B” 
Possible Venn diagrams.

syllogism-venn diagram

syllogism-venn diagram

Let us see whether following conclusions follows ‘ the above statement  or not. A Conclusion follows if and only if conclusion is satisfied in all possible conditions of the statement. That means conclusion must be possible in all Venn  diagrams we have drawn .
syllogism-venn diagram
You can see only conclusions 2 and 3  clearly  follows .But look at the conclusions 1 and 7,there is a possibility for these  conclusions to be true.If the conclusions 1 and 7 are modified as below
1=> All A being   B is a possibility(see fig.2). and
7=> Some B  not being  A is a possibility (see fig.1).
Then the answer will be’ YES’ and ‘YES’. Hope it is clear….Now let us go to next statement

2.Statement:”some A are B” 
Possible Venn diagrams.

syllogism-venn diagram




Let us see whether following conclusions follows the above statement or not.

You can see only conclusion 3 clearly follows. But in some cases there is possibility for conclusions 1,2,6 and 7 to be true. If we  modify 1,2,6 and 7 as follows.
1=> All A being B is a possibility.(see fig.4 and fig.6)
2=>All B being A is a possibility.(see fig.5 and fig.6)
6=>Some A not being B is a possibility(see fig.3 and fig.5)
7=>Some B not being A is a possibility(see fig.3 and fig.4)
Then these conclusions follows the statement.

3.Statement:"Some A are not B"
 Possible Venn diagrams.


None of the conclusion follows directly. But there exist possibility for conclusion 2 to 7.If we modify them
2=>All B being A is a possibility? YES (fig.8)
3=>Some B  being A is a possibility? YES(fig.7 and fig.8)
4=>No A being B is a possibility ?YES(fig.9).
5=> No B being  A is a possibility ?YES (fig.9).
6=> Some A being  B is possibility?YES(fig.7 and fig.8).
7=> Some B  not being  A is a possibility.?YES(fig.7 and fig.9).
Hope you understood ….

4.Statement:"No A is B"
Possible Venn diagram

syllogism-venn diagram

Conclusions 4,5 and 7 follows. In this case there is only one Venn diagram possible ,therefore there is no possibility cases.
Now let us do some simple problems.

Q1)Statement :Some Pens are Pencils.
                        All Pencils are Books.
Conclusions:1.All the Books are Pencil
                     2. Some Pens are Book.
                     3. All Pen being Book is a possibility.
syllogism-venn diagram


Q2)Statement:Some Dogs are Cat.
                       Some Cats are Cows.
 Conclusions:1.Some Dogs are Cows.
                     2. Some Cats are Dogs.


Q3):Statements:All cars are Chair.
                          No Chair is Mug.
Conclusions:1.No car is mug.
                     2.All Chair are cars.


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Click here to read solving 3,4 statement syllogism

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1 comment:

  1. Statement

    No fox is a cat
    No cat is a dog
    All monkeys are foxes

    No monkey is fox
    All dogs are definitely not cats
    Some foxes are not dogs

    which of following conclusions that does not follows?
    using venn diagram


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