Download as PDF

Syllogism:

“Syllogism” is defined as „interference‟ or „deduction‟. Syllogism has at least 4-5 questions in all competitive examination. So in this chapter our focus is to know about technique to solve problem.
First of all we have to understand the format of these types of questions. There are two parts in this type of question: Statements and Conclusions.

Format of this type of question:

1. Statements: All books are pen.
All pens are table.
Conclusion: A. All pens are books
B. No pens are book.

Answer: Chose the correct one from options given below
a) Only A follow
b) Only B follow
c) Both follow
d) Neither follow
e) Either A or B follow

Type of statement:

There is four type statement: (1) A-type (2) E-type (3) I-type (4) O-type.
Examples of this type of statement:

  • A-type: All are S
  • E-type: No S are U
  • I-type: Some S are U
  • O-type: Some S are not U.

Here S is called subject and U is called predicate

Statement Conversion Rule:

A-type can be converted to I-type
E-type when converted become E-type only
I-type when converted become I-type only
O-type cannot be converted.

Conclusion Draw Table:

First statement type

2nd statement type

Conclusion type

A

A

A

A

E

E

E

A

O*

E

I

O*

I

A

I

I

E

O

Here O * = Format is exactly same as O-type but subject and predicate are opposite to that of O-type.

Note: A+I = A+O = E+E = E+O = I+I = I+O = O+A = O+E = O+I = O+O = No conclusion.

Immediate interference or conversion:

We describe a question as immediate interference or conversion in two situations:

  1. If we get the conclusion directly from the given statement.
  2. If we get one of the conclusion from the other conclusion.

An example of immediate interference is given below;

  1. Statements: All books are pen.
    All pens are red.
    Conclusion: i) All books are red.
    ii) Some red are books.

Here A+A = A is applied from the draw conversion table to get the conclusion

i) All books are red.
But, „All books are red‟ (A-type) is convertible to „Some red are books‟ (I-type).
„Some red are books‟ is conclusion (ii).

Here we get one conclusion from the other.
One more example is given below;

2. Statement: All books are pens.
All pens are red.
Conclusion: i) All books are red.
ii) Some pens are books

Here conclusion „(ii) Some pens are books‟ is direct converted from statement „All books are pens‟.Because A-type is direct convertible to I-type.

Complementary Pair:

Complementary pair is of 3 types such that subject and predicate of the two conclusions is same.

(a)I-O type (b) A-O type (c) I-E type.

We may get complementary pair in conclusions of this type of question. You can understand this with the help of some example:

I-O type: i) Some pens are books.
ii) Some pens are not books.

A-O type: i) All pens are books.
ii) Some pens are not books.

I-E type: i) Some pens are books.
ii) No pens are books.

If we found complementary pair in conclusions answers choice always follow “either (i) or (ii) follows”.

Detailed analytical Method of solving:

Step I: Aligning of given sentences

In this step we have to align the sentences in proper sequence. In every syllogism question the two statements have a common term. So, first find out the common term and then aligned the statements ins uch a way that “predicate of the first statement must be the subject of the second statement”. The common term is the subject of the second and predicate of the first.

Statements: Some books are pen.
No pen is table.

Here “Pen” is the common term.

Step II: Use draw conclusion table
In this step using the draw conclusion table given before in this chapter to get the conclusion from the statements.
Step III: Check for immediate pair:
In this step we must check for immediate pairs if any according to the “Statement Conversion Rule” given before in this chapter.
Step IV: Check for complementary pair:
In this step check for any complementary pair in the conclusions. Complementary pairs are I-O type, A-O type and I-E type.

Directions: Chose the correct option from (1), (2), (3), (4) and (5).

1.If only conclusion (i) follow
2.If only conclusion (ii) follow
3.If either (i) or (ii) follow
4.If both follow
5.If neither (i) nor (ii) follow.

Example 1:
Statements: Some poets are goats.
Some goats are trees.
Conclusion: (i) Some poets are tree.
(ii) Some trees are goats.

Solution:
Here common term between two statements is „goats‟ and statements are already aligned.
Since both the two statements are of I-type, so according to the draw conclusion table,
I + I = no conclusion.
At this stage our answer is (5).
But we must check for immediate interference or conversion. Then we find that the statement “Some goats are trees” is directly converted to one of the conclusion “Some trees are goats”.
Now at this stage our answer is (2)

Now again we must check for any complementary pair. But there is no complementary pair in the conclusions.
So final answer is (2). Only conclusion (ii) is follow.

Example 2:
Statements: All mobiles are Samsung.
All tablets are Samsung.
Conclusion: (i) Some mobiles are tablets.
(ii) Some tablets are mobiles

Solution:
Here the common term is „Samsung‟. So we have to align the two statements as per rule. After alignment the two statements are,
All mobiles are Samsung. (A-type)
Some Samsung are tablets. (I-type)
Now, A + I = no conclusion

Now check for any immediate conversion. But there is no immediate conversion.
Also there is no complementary pair in the conclusion.
So final answer is (5). Neither of the conclusions follows.

Example 3:
Statements: (a) Some papers are nibs.
(b)No file is a cutter.
(c)Some files are papers.
Conclusions: (i) Some files are nibs.
(ii) Some papers are cutters.
(iii) Some files are not nibs.
(iv) Some nibs are papers.
Directions: Chose the correct one from (1), (2), (3), (4) and (5).

  1. Either (i) or (iii), and (ii) follow
  2. Either (i) or (iii), and (ii) follow
  3. Either (ii) or (iv), and (i) follow
  4. Either (ii) or (iv), and (iii) follow
  5. Either (ii) or (iv) , and either (i) or (iii) follow

Solution:

It is a three statements question. There are also 4 steps. These steps are illustrated as follows;

Step I:
In this step we must carefully chose two relevant statement from three. For this first step we should perform certain operation as given below,

  • First take a given conclusion.
  • Now see the subject and predicate of the chosen conclusion.
  • Now see which of the two statements have the subject and predicate.
  • Then find the common term between the two statements if any and align it such that predicate of the first statement must be the subject of the second statements. And if there is no common term the we have to follow a chain system.

Now take conclusions one by one.

Conclusion I:
“Some files are nibs”. Here subject is „files‟ and predicate is „nibs‟. We see that „files‟ is in the statement (c) and statement (b) and „nibs‟ is in the statement (a).

But there is no common term between statement (b) and (a).
And „papers‟ is the common term between statement (c) and (a).
So two relevant statements are (c) and (a).

Conclusion II:
“Some papers are cutters”. Here subject is „papers‟ and predicate is „cutters‟. We see that „papers‟ is in the statement (a) and (c). „Cutters‟ is in the statement (b).
But there is no common term between (a) and (b).
And „files‟ is the common term between (c) and (b).
So two relevant statements are (c) and (b).

Conclusion III:
“Some files are not nibs”. Here also subject is „files‟ and predicate is „nibs‟.
Subject and predicate is same as in Conclusion I.
So two relevant statements are (c) and (a).

Conclusion IV:
“Some nibs are paper”. Here subject is „nibs‟ and predicate is „paper‟. So we see that statement (a) has also same term but in reverse order.
So there is only one relevant statement (a).

Step II:
In this step we use draw conclusion table for correct conclusion from the relevant statement already got in the Step I.
Conclusion I:
Two relevant statements are (c) and (a). Now align these two statement such that predicate of the first is the subject of the second statement.

Some files are papers. (I-type)
Some papers are nibs. (I-type)
So, I + I = no conclusion.
So, Conclusion I is not valid.

Conclusion II:
Two relevant statements are (c) and (b). Now align these two statement such that predicate of the first is the subject of the second statement.
Some papers are files (I-type) [converted from “Some files are papers”]
No files is a cutter. (E-type).
So, I + E = O = Some papers are not cutters. (This is not Conclusion II)
So, Conclusion II not follows.
Conclusion III:
Two relevant statements are (c) and (a) same as in Conclusion I.
So I + I = no conclusion.

So conclusion III not follows.
Conclusion IV:
It has only one relevant statement (a). But we need two relevant statements for a valid conclusion.
So, after Step II we see that none of the conclusion is follows. So we must proceed to Step III and Step IV.
Step III:
Check for immediate interference or conversion.
Here we see that Conclusion IV is directly converted from the Statement (a).
So, Conclusion IV = “Some nibs are papers” follows.
Step IV:
In this step we must look for any complementary pair in the conclusions given in the question. So, we must search for A-O or I-O or I-E pairs in the conclusions if any.
In this question we see that Conclusion I and Conclusion III is I-O type complementary pair. So either I or III follows.
So, correct answer is (2) either I or III, and IV follow.

Chain System in three statement syllogism:

If we don‟t find any common term between two relevant statements in the Step I we must follow the chain system. You can understand this system with the help of an example:

 

Here above we see that the predicate „sedan‟ of the first statement is the subject of the second. And
predicate „expensive‟ of the second statement is subject of the first statement.

Possibility Case in Syllogism:

Format of this type of question is understood with the help of below example:

Statement: (a) All pens are books.
(b) All books are table.
(c) No table is chair.
Conclusion: (1) No book is chair
(2) Some pens being heat is a possibility.
To solve this type of question we need to remember some important facts given below:

  • If – All A are B then we can say Some B are not A is a possibility.
  • If Some B are not A the we can say – All A are B is a possibility.
  • If Some A are B then we can say- All A are B is a possibility and All B are A is a possibility.
  • No Conclusion = Any possibility true.

Example:
Statements: (a) Some mails are charts.
(b) All browsers are charts.
Conclusion: (1) All mails being browser is a possibility.
(2) No browser is mail.
Solution:
Here we must convert the second statement for proper alignment. So we get,
Some mails are charts. (E-type)
Some charts are browsers. (E-type)
So, from draw conclusion table,
E + E = No conclusion.
So Conclusion (2) does not follow.
But as per possibility rule, No conclusion = Any possibility is true.
So only Conclusion (1) is true.